Tank and Heat Exchanger Design (fluids.geometry)¶
This module contains functionality for calculating parameters about different geometrical forms that come up in engineering practice.
Implemented geometry objects are tanks, helical coils, cooling towers, air coolers, compact heat exchangers, and plate and frame heat exchangers.
Additional functionality for typical catalyst/adsorbent pellet shapes is also included.
For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker or contact the author at Caleb.Andrew.Bell@gmail.com.
Main Interfaces¶
- class fluids.geometry.TANK(D=None, L=None, horizontal=True, sideA=None, sideB=None, sideA_a=None, sideB_a=None, sideA_f=None, sideA_k=None, sideB_f=None, sideB_k=None, sideA_a_ratio=None, sideB_a_ratio=None, L_over_D=None, V=None)[source]¶
Bases:
object
Class representing tank volumes and levels. All parameters are also attributes.
- Parameters
- D
float
Diameter of the cylindrical section of the tank, [m]
- L
float
Length of the main cylindrical section of the tank, [m]
- horizontalbool,
optional
Whether or not the tank is a horizontal or vertical tank
- sideA
str
,optional
The left (or bottom for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’, ‘same’].
- sideB
str
,optional
The right (or top for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’, ‘same’].
- sideA_a
float
,optional
The distance the head as specified by sideA extends down or to the left from the main cylindrical section, [m]
- sideB_a
float
,optional
The distance the head as specified by sideB extends up or to the right from the main cylindrical section, [m]
- sideA_f
float
,optional
Dimensionless dish-radius parameter for side A; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- sideA_k
float
,optional
Dimensionless knuckle-radius parameter for side A; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- sideB_f
float
,optional
Dimensionless dish-radius parameter for side B; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- sideB_k
float
,optional
Dimensionless knuckle-radius parameter for side B; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- sideA_a_ratio
float
,optional
Ratio for a parameter; can be used instead of specifying an absolute value, [-]
- sideB_a_ratio
float
,optional
Ratio for a parameter; can be used instead of specifying an absolute value, [-]
- L_over_D
float
,optional
Ratio of length over diameter, used only when D and L are both unspecified but V is, [-]
- V
float
,optional
Volume of the tank; solved for if specified, using sideA_a_ratio/sideB_a_ratio, sideA, sideB, horizontal, and one of L_over_D, L, or D, [m^3]
- D
Notes
For torpsherical tank heads, the following f and k parameters are used in standards. The default is ASME F&D.
f
k
2:1 semi-elliptical
0.9
0.17
ASME F&D
1
0.06
ASME 80/6
0.8
0.06
ASME 80/10 F&D
0.8
0.1
DIN 28011
1
0.1
DIN 28013
0.8
0.154
For the following cases, numerical integrals are used.
V_horiz_spherical V_horiz_torispherical SA_partial_horiz_spherical_head SA_partial_horiz_ellipsoidal_head SA_partial_horiz_guppy_head SA_partial_horiz_torispherical_head
Examples
Total volume of a tank:
>>> TANK(D=1.2, L=4, horizontal=False).V_total 4.523893421169302
Volume of a tank at a given height:
>>> TANK(D=1.2, L=4, horizontal=False).V_from_h(.5) 0.5654866776461628
Height of liquid for a given volume:
>>> TANK(D=1.2, L=4, horizontal=False).h_from_V(.5) 0.442097064
Surface area of a tank with a conical head:
>>> T1 = TANK(V=10, L_over_D=0.7, sideB='conical', sideB_a=0.5) >>> T1.A, T1.A_sideA, T1.A_sideB, T1.A_lateral (24.94775907, 5.118555, 5.497246, 14.331956)
Solving for tank volumes, first horizontal, then vertical:
>>> TANK(D=10., horizontal=True, sideA='conical', sideB='conical', V=500).L 4.699531 >>> TANK(L=4.69953105701, horizontal=True, sideA='conical', sideB='conical', V=500).D 9.9999999 >>> TANK(L_over_D=0.469953105701, horizontal=True, sideA='conical', sideB='conical', V=500).L 4.6995310
>>> TANK(D=10., horizontal=False, sideA='conical', sideB='conical', V=500).L 4.699531 >>> TANK(L=4.69953105701, horizontal=False, sideA='conical', sideB='conical', V=500).D 9.99999999 >>> TANK(L_over_D=0.469953105701, horizontal=False, sideA='conical', sideB='conical', V=500).L 4.699531057
- Attributes
- h_max
float
Height of the tank, [m]
- V_total
float
Total volume of the tank as calculated [m^3]
- sideA_V
float
Volume of only sideA [m^3]
- sideB_V
float
Volume of only sideB [m^3]
- lateral_V
float
Volume of cylindrical section of tank [m^3]
- A
float
Total surface area of the tank, [m^2]
- A_sideA
float
Surface area of sideA, [m^2]
- A_sideB
float
Surface area of sideB, [m^2]
- A_lateral
float
Surface area of the lateral side, [m^2]
- A_sideA_extra
float
Additional surface area of sideA beyond that of a flat disk, [m^2]
- A_sideB_extra
float
Additional surface area of sideB beyond that of a flat disk, [m^2]
- tablebool
Whether or not a table of heights-volumes has been generated
- heights
ndarray
Array of heights between 0 and h_max, [m]
- volumes
ndarray
Array of volumes calculated from the heights, [m^3]
- c_forward
ndarray
Coefficients for the Chebyshev approximations in calculating V from h, [-]
- c_backward
ndarray
Coefficients for the Chebyshev approximations in calculating h from V, [-]
- h_max
Methods
A_cross_sectional
(h[, method])Method to calculate the cross-sectional liquid surface area from which gas can evolve in a fully defined tank given a specified height h.
SA_from_h
(h[, method])Method to calculate the volume of liquid in a fully defined tank given a specified height h.
V_from_h
(h[, method])Method to calculate the volume of liquid in a fully defined tank given a specified height h.
add_thickness
(thickness[, sideA_thickness, ...])Method to create a new tank instance with the same parameters as itself, except with an added thickness to it.
from_two_specs
(spec0, spec1[, spec0_name, ...])Method to create a new tank instance according to two specifications which are not direct geometry parameters.
h_from_V
(V[, method])Method to calculate the height of liquid in a fully defined tank given a specified volume of liquid in it V.
set_chebyshev_approximators
([deg_forward, ...])Method to derive and set coefficients for chebyshev polynomial function approximation of the height-volume and volume-height relationship.
set_misc
()Set more parameters, after the tank is better defined than in the __init__ function.
set_table
([n, dx])Method to set an interpolation table of liquids levels versus volumes in the tank, for a fully defined tank.
- A_cross_sectional(h, method='full')[source]¶
Method to calculate the cross-sectional liquid surface area from which gas can evolve in a fully defined tank given a specified height h. h must be under the maximum height. This is calculated by numeric differentiation for most cases.
- SA_from_h(h, method='full')[source]¶
Method to calculate the volume of liquid in a fully defined tank given a specified height h. h must be under the maximum height.
- V_from_h(h, method='full')[source]¶
Method to calculate the volume of liquid in a fully defined tank given a specified height h. h must be under the maximum height. If the method is ‘chebyshev’, and the coefficients have not yet been calculated, they are created by calling set_chebyshev_approximators.
- add_thickness(thickness, sideA_thickness=None, sideB_thickness=None)[source]¶
Method to create a new tank instance with the same parameters as itself, except with an added thickness to it. This is useful to obtain ex. the inside of a tank and the outside; their different in volumes is the volume of the shell, and could be used to determine weight.
- Parameters
- Returns
- TANK
TANK
Tank object, [-]
- TANK
Notes
Be careful not to specify a negative thickness larger than the heads’ lengths, or the head will become concave! The same applies to adding a thickness to convex heads - they can become convex.
- chebyshev = False¶
- static from_two_specs(spec0, spec1, spec0_name='V', spec1_name='A_cross', h=None, horizontal=True, sideA=None, sideB=None, sideA_a=None, sideB_a=None, sideA_f=None, sideA_k=None, sideB_f=None, sideB_k=None, sideA_a_ratio=None, sideB_a_ratio=None)[source]¶
Method to create a new tank instance according to two specifications which are not direct geometry parameters.
The allowable options are ‘V’, ‘SA’, ‘V_partial’, ‘SA_partial’, and ‘A_cross’, the later three of which require h to be specified.
- Parameters
- spec0
float
Goal for spec0_name, [-]
- spec1
float
Goal for spec1_name, [-]
- spec0_name
str
One of ‘V’, ‘SA’, ‘V_partial’, ‘SA_partial’, and ‘A_cross’ [-]
- spec1_name
str
One of ‘V’, ‘SA’, ‘V_partial’, ‘SA_partial’, and ‘A_cross’ [-]
- h
float
Height at which to calculate the specs, [m]
- horizontalbool,
optional
Whether or not the tank is a horizontal or vertical tank
- sideA
str
,optional
The left (or bottom for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’, ‘same’].
- sideB
str
,optional
The right (or top for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’, ‘same’].
- sideA_a
float
,optional
The distance the head as specified by sideA extends down or to the left from the main cylindrical section, [m]
- sideB_a
float
,optional
The distance the head as specified by sideB extends up or to the right from the main cylindrical section, [m]
- sideA_f
float
,optional
Dimensionless dish-radius parameter for side A; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- sideA_k
float
,optional
Dimensionless knuckle-radius parameter for side A; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- sideB_f
float
,optional
Dimensionless dish-radius parameter for side B; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- sideB_k
float
,optional
Dimensionless knuckle-radius parameter for side B; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- spec0
- Returns
- TANK
TANK
Tank object at solved specifications, [-]
- TANK
Notes
Limited testing has been done on this method. The bounds are D between 0.1 mm and 10 km, with L_D ratios of 1e-4 to 1e4.
- h_from_V(V, method='spline')[source]¶
Method to calculate the height of liquid in a fully defined tank given a specified volume of liquid in it V. V must be under the maximum volume. If the method is ‘spline’, and the interpolation table is not yet defined, creates it by calling the method set_table. If the method is ‘chebyshev’, and the coefficients have not yet been calculated, they are created by calling set_chebyshev_approximators.
- set_chebyshev_approximators(deg_forward=50, deg_backwards=200)[source]¶
Method to derive and set coefficients for chebyshev polynomial function approximation of the height-volume and volume-height relationship.
A single set of chebyshev coefficients is used for the entire height- volume and volume-height relationships respectively.
The forward relationship, V_from_h, requires far fewer coefficients in its fit than the reverse to obtain the same relative accuracy.
Optionally, deg_forward or deg_backwards can be set to None to try to automatically fit the series to machine precision.
- set_misc()[source]¶
Set more parameters, after the tank is better defined than in the __init__ function.
Notes
Two of D, L, and L_over_D must be known when this function runs. The other one is set from the other two first thing in this function. a_ratio parameters are used to calculate a values for the heads here, if applicable. Radius is calculated here. Maximum tank height is calculated here. V_total is calculated here.
- set_table(n=100, dx=None)[source]¶
Method to set an interpolation table of liquids levels versus volumes in the tank, for a fully defined tank. Normally run by the h_from_V method, this may be run prior to its use with a custom specification. Either the number of points on the table, or the vertical distance between steps may be specified.
- table = False¶
- fluids.geometry.V_tank(D, L, horizontal=True, sideA=None, sideB=None, sideA_a=0.0, sideB_a=0.0, sideA_f=None, sideA_k=None, sideB_f=None, sideB_k=None)[source]¶
Calculates the total volume of a vertical or horizontal tank with different head types.
- Parameters
- D
float
Diameter of the cylindrical section of the tank, [m]
- L
float
Length of the main cylindrical section of the tank, [m]
- horizontalbool,
optional
Whether or not the tank is a horizontal or vertical tank
- sideA
str
,optional
The left (or bottom for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’].
- sideB
str
,optional
The right (or top for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’].
- sideA_a
float
,optional
The distance the head as specified by sideA extends down or to the left from the main cylindrical section, [m]
- sideB_a
float
,optional
The distance the head as specified by sideB extends up or to the right from the main cylindrical section, [m]
- sideA_f
float
,optional
Dimensionless dish-radius parameter for side A; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- sideA_k
float
,optional
Dimensionless knuckle-radius parameter for side A; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- sideB_f
float
,optional
Dimensionless dish-radius parameter for side B; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- sideB_k
float
,optional
Dimensionless knuckle-radius parameter for side B; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- D
- Returns
Examples
>>> V_tank(D=1.5, L=5., horizontal=False, sideA='conical', ... sideB='conical', sideA_a=2., sideB_a=1.) (10.602875205865551, 1.1780972450961726, 0.5890486225480863, 8.835729338221293)
- fluids.geometry.V_from_h(h, D, L, horizontal=True, sideA=None, sideB=None, sideA_a=0, sideB_a=0, sideA_f=None, sideA_k=None, sideB_f=None, sideB_k=None)[source]¶
Calculates partially full volume of a vertical or horizontal tank with different head types according to [1].
- Parameters
- h
float
Height of the liquid in the tank, [m]
- D
float
Diameter of the cylindrical section of the tank, [m]
- L
float
Length of the main cylindrical section of the tank, [m]
- horizontalbool,
optional
Whether or not the tank is a horizontal or vertical tank
- sideA
str
,optional
The left (or bottom for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’].
- sideB
str
,optional
The right (or top for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’].
- sideA_a
float
,optional
The distance the head as specified by sideA extends down or to the left from the main cylindrical section, [m]
- sideB_a
float
,optional
The distance the head as specified by sideB extends up or to the right from the main cylindrical section, [m]
- sideA_f
float
,optional
Dimensionless dish-radius parameter for side A; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- sideA_k
float
,optional
Dimensionless knuckle-radius parameter for side A; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- sideB_f
float
,optional
Dimensionless dish-radius parameter for side B; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- sideB_k
float
,optional
Dimensionless knuckle-radius parameter for side B; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- h
- Returns
- V
float
Volume up to h [m^3]
- V
References
- 1
Jones, D. “Compute Fluid Volumes in Vertical Tanks.” Chemical Processing. December 18, 2003. http://www.chemicalprocessing.com/articles/2003/193/
Examples
>>> V_from_h(h=7, D=1.5, L=5., horizontal=False, sideA='conical', ... sideB='conical', sideA_a=2., sideB_a=1.) 10.013826583317465
- fluids.geometry.SA_tank(D, L, sideA=None, sideB=None, sideA_a=0, sideB_a=0, sideA_f=None, sideA_k=None, sideB_f=None, sideB_k=None)[source]¶
Calculates the surface are of a cylindrical tank with optional heads. In the degenerate case of being provided with only D and L, provides the surface area of a cylinder.
- Parameters
- D
float
Diameter of the cylindrical section of the tank, [m]
- L
float
Length of the main cylindrical section of the tank, [m]
- sideA
str
,optional
The left (or bottom for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’].
- sideB
str
,optional
The right (or top for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’].
- sideA_a
float
,optional
The distance the head as specified by sideA extends down or to the left from the main cylindrical section, [m]
- sideB_a
float
,optional
The distance the head as specified by sideB extends up or to the right from the main cylindrical section, [m]
- sideA_f
float
,optional
Dish-radius parameter for side A; fD = dish radius [1/m]
- sideA_k
float
,optional
knuckle-radius parameter for side A; kD = knuckle radius [1/m]
- sideB_f
float
,optional
Dish-radius parameter for side B; fD = dish radius [1/m]
- sideB_k
float
,optional
knuckle-radius parameter for side B; kD = knuckle radius [1/m]
- D
- Returns
Examples
Cylinder, Spheroid, Long Cones, and spheres. All checked.
>>> SA_tank(D=2, L=2)[0] 18.84955592153876 >>> SA_tank(D=1., L=0, sideA='ellipsoidal', sideA_a=2, sideB='ellipsoidal', ... sideB_a=2)[0] 10.124375616183062 >>> SA_tank(D=1., L=5, sideA='conical', sideA_a=2, sideB='conical', ... sideB_a=2)[0] 22.18452243965656 >>> SA_tank(D=1., L=5, sideA='spherical', sideA_a=0.5, sideB='spherical', ... sideB_a=0.5)[0] 18.84955592153876
- fluids.geometry.SA_from_h(h, D, L, horizontal=True, sideA=None, sideB=None, sideA_a=0.0, sideB_a=0.0, sideA_f=None, sideA_k=None, sideB_f=None, sideB_k=None)[source]¶
Calculates partially full wetted surface area of a vertical or horizontal tank with different head types according to [1].
- Parameters
- h
float
Height of the liquid in the tank, [m]
- D
float
Diameter of the cylindrical section of the tank, [m]
- L
float
Length of the main cylindrical section of the tank, [m]
- horizontalbool,
optional
Whether or not the tank is a horizontal or vertical tank
- sideA
str
,optional
The left (or bottom for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’].
- sideB
str
,optional
The right (or top for vertical) head of the tank’s type; one of [None, ‘conical’, ‘ellipsoidal’, ‘torispherical’, ‘guppy’, ‘spherical’].
- sideA_a
float
,optional
The distance the head as specified by sideA extends down or to the left from the main cylindrical section, [m]
- sideB_a
float
,optional
The distance the head as specified by sideB extends up or to the right from the main cylindrical section, [m]
- sideA_f
float
,optional
Dimensionless dish-radius parameter for side A; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- sideA_k
float
,optional
Dimensionless knuckle-radius parameter for side A; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- sideB_f
float
,optional
Dimensionless dish-radius parameter for side B; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- sideB_k
float
,optional
Dimensionless knuckle-radius parameter for side B; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- h
- Returns
- SA
float
Wetted wall surface area up to h [m^3]
- SA
References
- 1
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf http://www.chemicalprocessing.com/articles/2003/193/
Examples
>>> SA_from_h(h=7, D=1.5, L=5., horizontal=False, sideA='conical', ... sideB='conical', sideA_a=2., sideB_a=1.) 28.59477853914843
- class fluids.geometry.HelicalCoil(Dt, Do=None, pitch=None, H=None, N=None, H_total=None, Do_total=None, Di=None)[source]¶
Bases:
object
Class representing a helical coiled tube, as are found in many heated tanks and some small nuclear reactors. All parameters are also attributes.
One set of the following parameters is required; inner tube diameter is optional.
Tube outer diameter, coil outer diameter, pitch, number of coil turns
Tube outer diameter, coil outer diameter, pitch, height
Tube outer diameter, coil outer diameter, number of coil turns, height
- Parameters
- Dt
float
Outer diameter of the tube wound to make up the helical spiral, [m]
- Do
float
Diameter of the spiral as measured from the center of the coil on one side to the center of the coil on the other side, [m]
- Do_total
float
,optional
Diameter of the spiral as measured from one edge of the tube to the other edge; equal to Do + Dt; either Do or Do_total may be specified and the other will be calculated [m]
- pitch
float
,optional
Height change from one coil to the next as measured from the middles of the tube, [m]
- H
float
,optional
Height of the spiral, as measured from the middle of the bottom of the tube to the middle of the top of the tube, [m]
- H_total
float
,optional
Height of the spiral as measured from one edge of the tube to the other edge; equal to H_total + Dt; either may be specified and the other will be calculated [m]
- N
float
,optional
Number of coil turns; may be specified along with pitch instead of specifying H or H_total, [-]
- Di
float
,optional
Inner diameter of the tube; if specified, inside and annulus properties will be calculated, [m]
- Dt
Notes
Do must be larger than Dt.
References
- 1
El-Genk, Mohamed S., and Timothy M. Schriener. “A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes.” Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.
Examples
>>> C1 = HelicalCoil(Do=30, H=20, pitch=5, Dt=2) >>> C1.N, C1.tube_length, C1.surface_area (4.0, 377.5212621504738, 2372.0360474917497)
Same coil, with the inputs one would physically measure from the coil, and a specified inlet diameter:
>>> C1 = HelicalCoil(Do_total=32, H_total=22, pitch=5, Dt=2, Di=1.8) >>> C1.N, C1.tube_length, C1.surface_area (4.0, 377.5212621504738, 2372.0360474917497) >>> C1.inner_surface_area, C1.inlet_area, C1.inner_volume, C1.total_volume, C1.annulus_volume (2134.832442742575, 2.5446900494077327, 960.6745992341587, 1186.0180237458749, 225.3434245117162)
- Attributes
- tube_circumference
float
Circumference of the tube as measured though its center, not inner or outer edges; , [m]
- tube_length
float
Length of tube used to make the helical coil; , [m]
- surface_area
float
Surface area of the outer surface of the helical coil; , [m^2]
- inner_surface_area
float
Surface area of the inner surface of the helical coil; calculated if Di is supplied; , [m^2]
- inlet_area
float
Area of the inlet to the helical coil; calculated if Di is supplied; , [m^2]
- inner_volume
float
Volume of the tube as would be filled by a fluid, useful for weight calculations; calculated if Di is supplied; , [m^3]
- annulus_area
float
Area of the annulus (wall of the pipe); calculated if Di is supplied; , [m^2]
- annulus_volume
float
Volume of the annulus (wall of the pipe); calculated if Di is supplied, useful for weight calculations; , [m^3]
- total_volume
float
Total volume occupied by the pipe and the fluid inside it; , [m^3]
- helix_angle
float
Angle between the pitch and coil diameter; used in some calculations; , [radians]
- curvature
float
Coil curvature, useful in some calculations; , [-]
- tube_circumference
- class fluids.geometry.PlateExchanger(amplitude, wavelength, chevron_angle=45, chevron_angles=None, width=None, length=None, thickness=None, d_port=None, plates=None)[source]¶
Bases:
object
Class representing a plate heat exchanger with sinusoidal ridges. All parameters are also attributes.
- Parameters
- amplitude
float
Half the height of the wave of the ridges, [m]
- wavelength
float
Distance between the bottoms of two of the ridges (sometimes called pitch), [m]
- chevron_angle
float
,optional
Angle of the plate corrugations with respect to the vertical axis (the direction of flow if the plates were straight), between 0 and 90, [degrees]
- chevron_angles
tuple
(2),optional
Many plate exchangers use two alternating patterns; for those cases provide tuple of the two angles for that situation and the argument chevron_angle is ignored, [degrees]
- width
float
,optional
Width of the plates in the heat exchanger, between the gaskets, [m]
- length
float
,optional
Length of the heat exchanger as measured from one port to the other, excluding the diameter of the ports themselves (little useful heat transfer happens there), [m]
- thickness
float
,optional
Thickness of the metal making up the plates, [m]
- d_port
float
,optional
The diameter of the ports in the plates, [m]
- plates
int
,optional
The number of plates in the heat exchanger, including the two not used for heat transfer at the beginning and end [-]
- amplitude
Notes
Only wavelength and amplitude are required as inputs to this function.
References
- 1
Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome. “Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers. Part 1: Review and Experimental Database.” International Journal of Refrigeration 61 (January 2016): 166-84. doi:10.1016/j.ijrefrig.2015.07.010.
Examples
>>> PlateExchanger(amplitude=5E-4, wavelength=3.7E-3, length=1.2, width=.3, ... d_port=.05, plates=51) <Plate heat exchanger, amplitude=0.0005 m, wavelength=0.0037 m, chevron_angles=45/45 degrees, area enhancement factor=1.16119, width=0.3 m, length=1.2 m, port diameter=0.05 m, heat transfer area=20.4833 m^2, 51 plates>
- Attributes
- chevron_angles
tuple
(2) The two specified angles (repeated value if only one specified), [degrees]
- chevron_angle
float
The averaged angle of the chevrons, [degrees]
- inclination_angle
float
90 - chevron_angle, used in many publications instead of chevron_angle, [degrees]
- plate_corrugation_aspect_ratio
float
The aspect ratio of the corrugations , [-]
- plate_enlargement_factor
float
The extra surface area multiplier as compared to a flat plate caused the corrugations, [-]
- D_eq
float
Equivalent diameter of the channels, [m]
- D_hydraulic
float
Hydraulic diameter of the channels, [m]
- length_port
float
Port center to port center along the direction of flow, [m]
- A_plate_surface
float
The surface area of one plate in the heat exchanger, including the extra due to corrugations (excluding the bit between the ports), [m^2]
- A_heat_transfer
float
The total surface area available for heat transfer in the exchanger, the multiple of A_plate_surface by the number of plates after removing the two on the edges, [m^2]
- A_channel_flow
float
The area for the fluid to flow in one channel, [m^2]
- channels
int
The number of plates minus one, [-]
- channels_per_fluid
int
Half the number of total channels, [-]
- chevron_angles
- property plate_exchanger_identifier¶
Method to create an identifying string in format ‘L’ + wavelength + ‘A’ + amplitude + ‘B’ + chevron angle-chevron angle.
Wavelength and amplitude are specified in units of mm and rounded to two decimal places.
- class fluids.geometry.AirCooledExchanger(tube_rows, tube_passes, tubes_per_row, tube_length, tube_diameter, fin_thickness, angle=None, pitch=None, pitch_parallel=None, pitch_normal=None, pitch_ratio=None, fin_diameter=None, fin_height=None, fin_density=None, fin_interval=None, parallel_bays=1, bundles_per_bay=1, fans_per_bay=1, corbels=False, tube_thickness=None, fan_diameter=None)[source]¶
Bases:
object
Class representing the geometry of an air cooled heat exchanger with one or more tube bays, fans, or bundles. All parameters are also attributes.
The minimum information required to describe an air cooler is as follows:
tube_rows
tube_passes
tubes_per_row
tube_length
tube_diameter
fin_thickness
Two of angle, pitch, pitch_parallel, and pitch_normal (pitch_ratio may take the place of pitch)
Either fin_diameter or fin_height. Either fin_density or fin_interval.
- Parameters
- tube_rows
int
Number of tube rows per bundle, [-]
- tube_passes
int
Number of tube passes (times the fluid travels across one tube length), [-]
- tubes_per_row
float
Number of tubes per row per bundle, [-]
- tube_length
float
Total length of the tube bundle tubes, [m]
- tube_diameter
float
Diameter of the bare tube, [m]
- fin_thickness
float
Thickness of the fins, [m]
- angle
float
,optional
Angle of the tube layout, [degrees]
- pitch
float
,optional
Shortest distance between tube centers; defined in relation to the flow direction only, [m]
- pitch_parallel
float
,optional
Distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]
- pitch_normal
float
,optional
Distance between tube centers in a line 90° to the line of flow; has been called the transverse pitch, pn, s1, ST, and p1, [m]
- pitch_ratio
float
,optional
Ratio of the pitch to bare tube diameter, [-]
- fin_diameter
float
,optional
Outer diameter of each tube after including the fin on both sides, [m]
- fin_height
float
,optional
Height above bare tube of the tube fins, [m]
- fin_density
float
,optional
Number of fins per meter of tube, [1/m]
- fin_interval
float
,optional
Space between each fin, including the thickness of one fin at its base, [m]
- parallel_bays
int
,optional
Number of bays in the unit, [-]
- bundles_per_bay
int
,optional
Number of tube bundles per bay, [-]
- fans_per_bay
int
,optional
Number of fans per bay, [-]
- corbelsbool,
optional
Whether or not the air cooler has corbels, which increase the air velocity by adding half a tube to the sides for the case of non-rectangular tube layouts, [-]
- tube_thickness
float
,optional
Thickness of the bare metal tubes, [m]
- fan_diameter
float
,optional
Diameter of air cooler fan, [m]
- tube_rows
References
- 1
Schlunder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1983.
Examples
>>> from scipy.constants import inch >>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=56, tube_length=10.9728, ... tube_diameter=1*inch, fin_thickness=0.013*inch, fin_density=10/inch, ... angle=30, pitch=2.5*inch, fin_height=0.625*inch, tube_thickness=0.00338, ... bundles_per_bay=2, parallel_bays=3, corbels=True)
- Attributes
- bare_length
float
Length of bare tube between two fins , [m]
- tubes_per_bundle
float
Total number of tubes per bundle , [-]
- tubes_per_bay
float
Total number of tubes per bay , [-]
- tubes
float
Total number of tubes in all bundles in all bays combined , [-]
- pitch_diagonal
float
Distance between tube centers in a diagonal line between one normal tube and one parallel tube; , [m]
- A_bare_tube_per_tube
float
Area of the bare tube including the portion hidden by the fin per tube , [m^2]
- A_bare_tube_per_row
float
Area of the bare tube including the portion hidden by the fin per tube row , [m^2]
- A_bare_tube_per_bundle
float
Area of the bare tube including the portion hidden by the fin per bundle , [m^2]
- A_bare_tube_per_bay
float
Area of the bare tube including the portion hidden by the fin per bay , [m^2]
- A_bare_tube
float
Area of the bare tube including the portion hidden by the fin per in all bundles and bays combined , [m^2]
- A_tube_showing_per_tube
float
Area of the bare tube which is exposed per tube , [m^2]
- A_tube_showing_per_row
float
Area of the bare tube which is exposed per tube row, [m^2]
- A_tube_showing_per_bundle
float
Area of the bare tube which is exposed per bundle, [m^2]
- A_tube_showing_per_bay
float
Area of the bare tube which is exposed per bay, [m^2]
- A_tube_showing
float
Area of the bare tube which is exposed in all bundles and bays combined, [m^2]
- A_per_fin
float
Surface area per fin , [m^2]
- A_fin_per_tube
float
Surface area of all fins per tube , [m^2]
- A_fin_per_row
float
Surface area of all fins per row, [m^2]
- A_fin_per_bundle
float
Surface area of all fins per bundle, [m^2]
- A_fin_per_bay
float
Surface area of all fins per bay, [m^2]
- A_fin
float
Surface area of all fins in all bundles and bays combined, [m^2]
- A_per_tube
float
Surface area of combined finned and non-fined area exposed for heat transfer per tube , [m^2]
- A_per_row
float
Surface area of combined finned and non-finned area exposed for heat transfer per tube row, [m^2]
- A_per_bundle
float
Surface area of combined finned and non-finned area exposed for heat transfer per tube bundle, [m^2]
- A_per_bay
float
Surface area of combined finned and non-finned area exposed for heat transfer per bay, [m^2]
- A
float
Surface area of combined finned and non-finned area exposed for heat transfer in all bundles and bays combined, [m^2]
- A_increase
float
Ratio of actual surface area to bare tube surface area , [-]
- A_tube_flow
float
The area for the fluid to flow in one tube, , [m^2]
- channels
int
The number of tubes the fluid flows through at the inlet header, [-]
- tube_volume_per_tube
float
Fluid volume per tube inside , [m^3]
- tube_volume_per_row
float
Fluid volume of tubes per row, [m^3]
- tube_volume_per_bundle
float
Fluid volume of tubes per bundle, [m^3]
- tube_volume_per_bay
float
Fluid volume of tubes per bay, [m^3]
- tube_volume
float
Fluid volume of tubes in all bundles and bays combined, [m^3]
- A_diagonal_per_bundle
float
Air flow area along the diagonal plane per bundle , [m^2]
- A_normal_per_bundle
float
Air flow area along the normal (transverse) plane; this is normally the minimum flow area, except for some staggered configurations , [m^2]
- A_min_per_bundle
float
Minimum air flow area per bundle; this is the characteristic area for velocity calculation in most finned tube convection correlations , [m^2]
- A_min_per_bay
float
Minimum air flow area per bay, [m^2]
- A_min
float
Minimum air flow area, [m^2]
- A_face_per_bundle
float
Face area per bundle ; if corbels are used, add 0.5 to tubes/row instead of 1, [m^2]
- A_face_per_bay
float
Face area per bay, [m^2]
- A_face
float
Total face area, [m^2]
- flow_area_contraction_ratio
float
Ratio of A_min to A_face, [-]
- bare_length
- class fluids.geometry.HyperbolicCoolingTower(H_inlet, D_outlet, H_outlet, D_inlet=None, D_base=None, D_throat=None, H_throat=None, H_support=None, D_support=None, n_support=None, inlet_rounding=None)[source]¶
Bases:
object
Class representing the geometry of a hyperbolic cooling tower, as used in many industries especially the poewr industry. All parameters are also attributes.
H_inlet, D_outlet, and H_outlet are always required. Additionally, one set of the following parameters is required; H_support, D_support, n_support, and inlet_rounding are all optional as well.
Inlet diameter
Inlet diameter and throat diameter
Inlet diameter and throat height
Inlet diameter, throat diameter, and throat height
Base diameter, throat diameter, and throat height
If the inlet diameter is provided but the throat diameter and/or the throat height are missing, two heuristics are used to estimate them (to avoid these heuristics simply specify the values):
Assume the throat elevation is 2/3 the elevation of the tower.
Assume the throat diameter is 63% the diameter of the inlet.
- Parameters
- H_inlet
float
Height of the inlet zone of the cooling tower (also called rain zone), [m]
- D_outlet
float
The inside diameter of the cooling tower outlet (top of the tower; the elevation the concrete section ends), [m]
- H_outlet
float
The height of the cooling tower outlet (top of the tower;the elevation the concrete section ends), [m]
- D_inlet
float
,optional
The inside diameter of the cooling tower inlet at the elevation the concrete section begins, [m]
- D_base
float
,optional
The diameter of the cooling tower at the very base of the tower (the bottom of the inlet zone, at the elevation of the ground), [m]
- D_throat
float
,optional
The diameter of the cooling tower at its minimum section, called its throat; where the two hyperbolas meet, [m]
- h_throat
float
,optional
The elevation of the cooling tower’s throat (its minimum section; where the two hyperbolas meet), [m]
- inlet_rounding
float
,optional
Radius of an optional rounded protrusion from the lip of the cooling tower shell base, which curves upwards from the lip (used to reduce the dead zone area rather than having a flat lip), [m]
- H_support
float
,optional
The height of each support column, [m]
- D_support
float
,optional
The diameter of each support column, [m]
- n_support
int
,optional
The number of support columns of the cooling tower, [m]
- H_inlet
Notes
Note there are two hyperbolas in a hyperbolic cooling tower - one under the throat and one above it; they are not necessarily the same.
A hyperbolic cooling tower is not the absolute optimal design, but is is close. The optimality is determined by the amount of material required to build it while maintaining its rigidity. For thermal design purposes, a hyperbolic model covers any minor variation quite well.
References
- 1
Chen, W. F., and E. M. Lui, eds. Handbook of Structural Engineering, Second Edition. Boca Raton, Fla: CRC Press, 2005.
- 2
Ansary, A. M. El, A. A. El Damatty, and A. O. Nassef. Optimum Shape and Design of Cooling Towers, 2011.
Examples
>>> ct = HyperbolicCoolingTower(D_outlet=89.0, H_outlet=200, D_inlet=136.18, H_inlet=14.5) >>> ct <Hyperbolic cooling tower, inlet diameter=136.18 m, outlet diameter=89 m, inlet height=14.5 m, outlet height=200 m, throat diameter=85.7934 m, throat height=133.333 m, base diameter=146.427 m> >>> ct.diameter(5) 142.84514486126062
- Attributes
Methods
diameter
(H)Calculates cooling tower diameter at a specified height, using the formulas for either hyperbola, depending on the height specified.
plot
- diameter(H)[source]¶
Calculates cooling tower diameter at a specified height, using the formulas for either hyperbola, depending on the height specified.
The value of H and b used in the above equation is as follows:
H_throat - H and b_lower if under the throat
H - H_throat and b_upper, if above the throat
- class fluids.geometry.RectangularFinExchanger(fin_height, fin_thickness, fin_spacing, length=None, width=None, layers=None, plate_thickness=None, flow='crossflow')[source]¶
Bases:
object
Class representing a plate-fin heat exchanger with straight rectangular fins. All parameters are also attributes.
- Parameters
- fin_height
float
The total distance between the two metal plates sandwiching the fins and holding them together (abbreviated h), [m]
- fin_thickness
float
The thickness of the material the fins were formed from (abbreviated t), [m]
- fin_spacing
float
The unit cell spacing from one fin to the next; the space between the sides of two fins plus one thickness (abbreviated s), [m]
- length
float
,optional
The total length of the flow passage of the plate-fin exchanger (abbreviated L), [m]
- width
float
,optional
The total width of the space the fins are in; this is also (abbreviated W), [m]
- layers
int
,optional
The number of layers in the plate-fin exchanger; note these HX almost always single-pass only, [-]
- plate_thickness
float
,optional
The thickness of the metal separator between layers, [m]
- flow
str
,optional
One of ‘counterflow’, ‘crossflow’, or ‘parallelflow’
- fin_height
Notes
The only required parameters are the fin geometry itself; fin_height, fin_thickness, and fin_spacing.
References
- 1
Yang, Yujie, and Yanzhong Li. “General Prediction of the Thermal Hydraulic Performance for Plate-Fin Heat Exchanger with Offset Strip Fins.” International Journal of Heat and Mass Transfer 78 (November 1, 2014): 860-70. doi:10.1016/j.ijheatmasstransfer.2014.07.060.
- 2
Sheik Ismail, L., R. Velraj, and C. Ranganayakulu. “Studies on Pumping Power in Terms of Pressure Drop and Heat Transfer Characteristics of Compact Plate-Fin Heat Exchangers-A Review.” Renewable and Sustainable Energy Reviews 14, no. 1 (January 2010): 478-85. doi:10.1016/j.rser.2009.06.033.
Examples
>>> PFE = RectangularFinExchanger(0.03, 0.001, 0.012) >>> PFE.Dh 0.01595
- Attributes
- channel_height
float
The height of the channel the fluid flows in , [m]
- channel_width
float
The width of the channel the fluid flows in , [m]
- fin_count
int
The number of fins per unit length of the layer, , [1/m]
- blockage_ratio
float
The fraction of the layer which is blocked to flow by the fins, , [m]
- A_channel
float
Flow area of a single channel in a single layer, , [m]
- P_channel
float
Wetted perimeter of a single channel in a single layer, , [m]
- Dh
float
Hydraulic diameter of a single channel in a single layer, , [m]
- layer_thickness
float
The thickness of a single layer - the sum of a fin height and a plate thickness, [m]
- layer_fin_count
int
The number of fins in a layer; rounded to the nearest whole fin, [-]
- A_HX_layer
float
The surface area including fins for heat transfer in one layer of the HX, [m^2]
- A_HX
float
The total surface area of the heat exchanger with all layers combined, [m^2]
- height
float
The height of all the layers of the heat exchanger combined, plus one extra plate thickness, [m]
- volume
float
The product of the height, width, and length of the HX, [m^3]
- A_specific_HX
float
The specific surface area of the heat exchanger - square meters per meter cubed, [m^3]
- channel_height
Methods
set_overall_geometry
- class fluids.geometry.RectangularOffsetStripFinExchanger(fin_length, fin_height, fin_thickness, fin_spacing, length=None, width=None, layers=None, plate_thickness=None, flow='crossflow')[source]¶
Bases:
fluids.geometry.RectangularFinExchanger
Methods
set_overall_geometry
Tank Volume Functions¶
- fluids.geometry.V_partial_sphere(D, h)[source]¶
Calculates volume of a partial sphere according to [1]. If h is half of D, the shape is half a sphere. No bottom is considered in this function. Valid inputs are positive values of D and h, with h always smaller or equal to D.
- Parameters
- Returns
- V
float
Volume [m^3]
- V
References
- 1
Weisstein, Eric W. “Spherical Cap.” Text. Accessed December 22, 2015. http://mathworld.wolfram.com/SphericalCap.html.
Examples
>>> V_partial_sphere(1., 0.7) 0.4105014400690663
- fluids.geometry.V_horiz_conical(D, L, a, h, headonly=False)[source]¶
Calculates volume of a tank with conical ends, according to [1].
- Parameters
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Calculating Tank Volume.” Text. Accessed December 22, 2015. http://www.webcalc.com.br/blog/Tank_Volume.PDF
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_horiz_conical(D=108., L=156., a=42., h=36)/231 2041.1923581273443
- fluids.geometry.V_horiz_ellipsoidal(D, L, a, h, headonly=False)[source]¶
Calculates volume of a tank with ellipsoidal ends, according to [1].
- Parameters
- D
float
Diameter of the main cylindrical section, [m]
- L
float
Length of the main cylindrical section, [m]
- a
float
Distance the ellipsoidal head extends on one side, [m]
- h
float
Height, as measured up to where the fluid ends, [m]
- headonlybool,
optional
Function returns only the volume of a single head side if True
- D
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Calculating Tank Volume.” Text. Accessed December 22, 2015. http://www.webcalc.com.br/blog/Tank_Volume.PDF
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_horiz_ellipsoidal(D=108, L=156, a=42, h=36)/231. 2380.9565415578145
- fluids.geometry.V_horiz_guppy(D, L, a, h, headonly=False)[source]¶
Calculates volume of a tank with guppy heads, according to [1].
- Parameters
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Calculating Tank Volume.” Text. Accessed December 22, 2015. http://www.webcalc.com.br/blog/Tank_Volume.PDF
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_horiz_guppy(D=108., L=156., a=42., h=36)/231. 1931.7208029476762
- fluids.geometry.V_horiz_spherical(D, L, a, h, headonly=False)[source]¶
Calculates volume of a tank with spherical heads, according to [1].
- Parameters
- D
float
Diameter of the main cylindrical section, [m]
- L
float
Length of the main cylindrical section, [m]
- a
float
Distance the spherical head extends on one side, [m]
- h
float
Height, as measured up to where the fluid ends, [m]
- headonlybool,
optional
Function returns only the volume of a single head side if True
- D
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Calculating Tank Volume.” Text. Accessed December 22, 2015. http://www.webcalc.com.br/blog/Tank_Volume.PDF
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_horiz_spherical(D=108., L=156., a=42., h=36)/231. 2303.9615116986183
- fluids.geometry.V_horiz_torispherical(D, L, f, k, h, headonly=False)[source]¶
Calculates volume of a tank with torispherical heads, according to [1].
- Parameters
- D
float
Diameter of the main cylindrical section, [m]
- L
float
Length of the main cylindrical section, [m]
- f
float
Dimensionless dish-radius parameter; also commonly given as the product of f and D (fD), which is called both dish radius and also crown radius and has units of length, [-]
- k
float
Dimensionless knuckle-radius parameter; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- h
float
Height, as measured up to where the fluid ends, [m]
- headonlybool,
optional
Function returns only the volume of a single head side if True
- D
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Calculating Tank Volume.” Text. Accessed December 22, 2015. http://www.webcalc.com.br/blog/Tank_Volume.PDF
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_horiz_torispherical(D=108., L=156., f=1., k=0.06, h=36)/231. 2028.62667
- fluids.geometry.V_vertical_conical(D, a, h)[source]¶
Calculates volume of a vertical tank with a convex conical bottom, according to [1]. No provision for the top of the tank is made here.
- Parameters
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Calculating Tank Volume.” Text. Accessed December 22, 2015. http://www.webcalc.com.br/blog/Tank_Volume.PDF
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_vertical_conical(132., 33., 24)/231. 250.67461381371024
- fluids.geometry.V_vertical_ellipsoidal(D, a, h)[source]¶
Calculates volume of a vertical tank with a convex ellipsoidal bottom, according to [1]. No provision for the top of the tank is made here.
- Parameters
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Calculating Tank Volume.” Text. Accessed December 22, 2015. http://www.webcalc.com.br/blog/Tank_Volume.PDF
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_vertical_ellipsoidal(132., 33., 24)/231. 783.3581681678445
- fluids.geometry.V_vertical_spherical(D, a, h)[source]¶
Calculates volume of a vertical tank with a convex spherical bottom, according to [1]. No provision for the top of the tank is made here.
- Parameters
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Calculating Tank Volume.” Text. Accessed December 22, 2015. http://www.webcalc.com.br/blog/Tank_Volume.PDF
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_vertical_spherical(132., 33., 24)/231. 583.6018352850442
- fluids.geometry.V_vertical_torispherical(D, f, k, h)[source]¶
Calculates volume of a vertical tank with a convex torispherical bottom, according to [1]. No provision for the top of the tank is made here.
- Parameters
- D
float
Diameter of the main cylindrical section, [m]
- f
float
Dimensionless dish-radius parameter; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- k
float
Dimensionless knuckle-radius parameter; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- h
float
Height, as measured up to where the fluid ends, [m]
- D
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Calculating Tank Volume.” Text. Accessed December 22, 2015. http://www.webcalc.com.br/blog/Tank_Volume.PDF
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_vertical_torispherical(D=132., f=1.0, k=0.06, h=24)/231. 904.0688283793
- fluids.geometry.V_vertical_conical_concave(D, a, h)[source]¶
Calculates volume of a vertical tank with a concave conical bottom, according to [1]. No provision for the top of the tank is made here.
- Parameters
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Compute Fluid Volumes in Vertical Tanks.” Chemical Processing. December 18, 2003. http://www.chemicalprocessing.com/articles/2003/193/
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_vertical_conical_concave(D=113., a=-33, h=15)/231 251.15825565795188
- fluids.geometry.V_vertical_ellipsoidal_concave(D, a, h)[source]¶
Calculates volume of a vertical tank with a concave ellipsoidal bottom, according to [1]. No provision for the top of the tank is made here.
- Parameters
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Compute Fluid Volumes in Vertical Tanks.” Chemical Processing. December 18, 2003. http://www.chemicalprocessing.com/articles/2003/193/
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_vertical_ellipsoidal_concave(D=113., a=-33, h=15)/231 44.84968851034856
- fluids.geometry.V_vertical_spherical_concave(D, a, h)[source]¶
Calculates volume of a vertical tank with a concave spherical bottom, according to [1]. No provision for the top of the tank is made here.
- Parameters
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Compute Fluid Volumes in Vertical Tanks.” Chemical Processing. December 18, 2003. http://www.chemicalprocessing.com/articles/2003/193/
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_vertical_spherical_concave(D=113., a=-33, h=15)/231 112.81405437348528
- fluids.geometry.V_vertical_torispherical_concave(D, f, k, h)[source]¶
Calculates volume of a vertical tank with a concave torispherical bottom, according to [1]. No provision for the top of the tank is made here.
- Parameters
- D
float
Diameter of the main cylindrical section, [m]
- f
float
Dimensionless dish-radius parameter; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- k
float
Dimensionless knuckle-radius parameter; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- h
float
Height, as measured up to where the fluid ends, [m]
- D
- Returns
- V
float
Volume [m^3]
- V
References
- 1(1,2)
Jones, D. “Compute Fluid Volumes in Vertical Tanks.” Chemical Processing. December 18, 2003. http://www.chemicalprocessing.com/articles/2003/193/
Examples
Matching example from [1], with inputs in inches and volume in gallons.
>>> V_vertical_torispherical_concave(D=113., f=0.71, k=0.081, h=15)/231 103.88569287163769
Tank Surface Area Functions¶
- fluids.geometry.SA_partial_sphere(D, h)[source]¶
Calculates surface area of a partial sphere according to [1]. If h is half of D, the shape is half a sphere. No bottom is considered in this function. Valid inputs are positive values of D and h, with h always smaller or equal to D.
- Parameters
- Returns
- SA
float
Surface area [m^2]
- SA
References
- 1
Weisstein, Eric W. “Spherical Cap.” Text. Accessed December 22, 2015. http://mathworld.wolfram.com/SphericalCap.html.
Examples
>>> SA_partial_sphere(1., 0.7) 2.199114857512855
- fluids.geometry.SA_ellipsoidal_head(D, a)[source]¶
Calculates the surface area of an ellipsoidal head according to [1] and [2]. The formula below is for the full shape, the result of which is halved. The formula is for . In the equations, a is the same and c is D.
For the case of from [2], which is needed to make the tank head volume grow linearly with length:
- Parameters
- Returns
- SA
float
Surface area [m^2]
- SA
References
- 1
Weisstein, Eric W. “Spheroid.” Text. Accessed March 14, 2016. http://mathworld.wolfram.com/Spheroid.html.
- 2(1,2)
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf
Examples
Spherical case
>>> SA_ellipsoidal_head(2, 1) 6.283185307179586 >>> SA_ellipsoidal_head(2, 1.5) 8.459109081729984
- fluids.geometry.SA_conical_head(D, a)[source]¶
Calculates the surface area of a conical head according to [1].
- Parameters
- Returns
- SA
float
Surface area [m^2]
- SA
References
- 1
Weisstein, Eric W. “Cone.” Text. Accessed March 14, 2016. http://mathworld.wolfram.com/Cone.html.
Examples
>>> SA_conical_head(2, 1) 4.442882938158366
- fluids.geometry.SA_guppy_head(D, a)[source]¶
Calculates the surface area of a guppy head according to [1]. Some work was involved in combining formulas for the ellipse of the head, and the conic section on the sides.
- Parameters
- Returns
- SA
float
Surface area [m^2]
- SA
References
- 1
Weisstein, Eric W. “Cone.” Text. Accessed March 14, 2016. http://mathworld.wolfram.com/Cone.html.
Examples
>>> SA_guppy_head(2, 1) 6.654000019110157
- fluids.geometry.SA_torispheroidal(D, f, k)[source]¶
Calculates surface area of a torispherical head according to [1]. Somewhat involved. Equations are adapted to be used for a full head.
- Parameters
- D
float
Diameter of the main cylindrical section, [m]
- f
float
Dimensionless dish-radius parameter; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- k
float
Dimensionless knuckle-radius parameter; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- D
- Returns
- SA
float
Surface area [m^2]
- SA
References
- 1(1,2)
Honeywell. “Calculate Surface Areas and Cross-sectional Areas in Vessels with Dished Heads”. https://www.honeywellprocess.com/library/marketing/whitepapers/WP-VesselsWithDishedHeads-UniSimDesign.pdf Whitepaper. 2014.
Examples
Example from [1].
>>> SA_torispheroidal(D=2.54, f=1.039370079, k=0.062362205) 6.00394283477063
- fluids.geometry.SA_partial_cylindrical_body(L, D, h)[source]¶
Calculates the partial area of a cylinder’s body in the context of a horizontal cylindrical vessel and liquid partially filling it. This computes the wetted surface area of the bottom of the cylinder.
- Parameters
- Returns
- SA_partial
float
Partial (wetted) surface area, [m^2]
- SA_partial
Notes
This method is undefined for . and , but those cases are handled by returning the full surface area and the zero respectively.
References
- 1
Weisstein, Eric W. “Circular Segment.” Text. Wolfram Research, Inc. Accessed May 10, 2020. https://mathworld.wolfram.com/CircularSegment.html.
Examples
>>> SA_partial_cylindrical_body(L=200.0, D=96., h=22.0) 19168.852890279868
- fluids.geometry.SA_partial_horiz_conical_head(D, a, h)[source]¶
Calculates the partial area of a conical tank head in the context of a horizontal vessel and liquid partially filling it. This computes the wetted surface area of one of the conical heads only.
- Parameters
- Returns
- SA_partial
float
Partial (wetted) surface area of one conical tank head, [m^2]
- SA_partial
Notes
This method is undefined for and , but those cases are handled by returning the full surface area and the zero respectively.
References
- 1
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf
Examples
>>> SA_partial_horiz_conical_head(D=72., a=48.0, h=24.0) 1980.0498315169873
- fluids.geometry.SA_partial_horiz_spherical_head(D, a, h)[source]¶
Calculates the partial area of a spherical tank head in the context of a horizontal vessel and liquid partially filling it. This computes the wetted surface area of one of the spherical heads only.
For the special case of :
- Parameters
- Returns
- SA_partial
float
Partial (wetted) surface area of one spherical tank head, [m^2]
- SA_partial
Notes
This method is undefined for and , but those cases are handled by returning the full surface area and the zero respectively.
A symbolic attempt did not suggest any analytical integrals were available.
References
- 1
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf
Examples
>>> SA_partial_horiz_spherical_head(D=72., a=48.0, h=24.0) 2027.2672
- fluids.geometry.SA_partial_horiz_ellipsoidal_head(D, a, h)[source]¶
Calculates the partial area of a ellipsoidal tank head in the context of a horizontal vessel and liquid partially filling it. This computes the wetted surface area of one of the ellipsoidal heads only.
After extensive manipulation, the first integral was solved analytically, extending the result of [1] with greater performance.
Where is the complete elliptic integral of the second kind, calculated with SciPy’s link to the cephes library.
- Parameters
- Returns
- SA_partial
float
Partial (wetted) surface area of one ellipsoidal tank head, [m^2]
- SA_partial
Notes
This method is undefined for and , but those cases are handled by returning the full surface area and the zero respectively.
The original numerical double integral is extremely nasty - there are places where f(x) -> infinity but that have a bounded area. quadpack’s numerical integration handles this well, but adaptive inetgration which is not aware of singularities does not.
References
- 1
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf
Examples
>>> SA_partial_horiz_ellipsoidal_head(D=72., a=48.0, h=24.0) 3401.233622547
- fluids.geometry.SA_partial_horiz_guppy_head(D, a, h)[source]¶
Calculates the partial area of a guppy tank head in the context of a horizontal vessel and liquid partially filling it. This computes the wetted surface area of one of the guppy heads only.
After extensive manipulation, the first integral was solved analytically, extending the result of [1]. Even with the special functions, this form has somewhat greater performance (and improved precision).
Where ellipeinc is the incomplete elliptic integral of the second kind, and ellipkinc is the incomplete elliptic integral of the first kind, both calculated with SciPy’s link to the cephes library.
- Parameters
- Returns
- SA_partial
float
Partial (wetted) surface area of one guppy tank head, [m^2]
- SA_partial
Notes
This method is undefined for and , but those cases are handled by returning the full surface area and the zero respectively.
The analytical integral was derived with Rubi.
References
- 1
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf
Examples
>>> SA_partial_horiz_guppy_head(D=72., a=48.0, h=24.0) 1467.8949
- fluids.geometry.SA_partial_horiz_torispherical_head(D, f, k, h)[source]¶
Calculates the partial area of a torispherical tank head in the context of a horizontal vessel and liquid partially filling it. This computes the wetted surface area of one of the torispherical heads only.
The expressions used are quite complicated; see [1] for more details.
- Parameters
- D
float
Diameter of the main cylindrical section, [m]
- f
float
Dimensionless dish-radius parameter; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- k
float
Dimensionless knuckle-radius parameter; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- h
float
Height, as measured up to where the fluid ends, [m]
- D
- Returns
- SA_partial
float
Partial (wetted) surface area of one torispherical tank head, [m^2]
- SA_partial
Notes
This method is undefined for and , but those cases are handled by returning the full surface area and the zero respectively.
One integral:
Can be computed as follows, using WolframAlpha.
With the following constants:
The other integral is a double integral. There is an analytical integral available for the first integral, which takes the form:
References
- 1
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf
Examples
>>> SA_partial_horiz_torispherical_head(D=72., f=1, k=.06, h=24.0) 1471.201832459
- fluids.geometry.SA_partial_vertical_conical_head(D, a, h)[source]¶
Calculates the partial area of a conical tank head in the context of a vertical vessel and liquid partially filling it. This computes the wetted surface area of one of the conical heads only, and is valid for h up to a only.
- Parameters
- Returns
- SA_partial
float
Partial (wetted) surface area of one conical tank head extending beneath the vessel, [m^2]
- SA_partial
Notes
This method is undefined for , but this is handled by returning zero.
References
- 1
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf
Examples
>>> SA_partial_vertical_conical_head(D=72., a=48.0, h=24.0) 1696.4600329384882
- fluids.geometry.SA_partial_vertical_ellipsoidal_head(D, a, h)[source]¶
Calculates the partial area of a ellipsoidal tank head in the context of a vertical vessel and liquid partially filling it. This computes the wetted surface area of one of the ellipsoidal heads only, and is valid for h up to a only.
If :
Otherwise for :
- Parameters
- Returns
- SA_partial
float
Partial (wetted) surface area of one ellipsoidal tank head extending beneath the vessel, [m^2]
- SA_partial
Notes
This method is undefined for , but this is handled by returning zero.
References
- 1
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf
Examples
>>> SA_partial_vertical_ellipsoidal_head(D=72., a=48.0, h=24.0) 4675.23789137632
- fluids.geometry.SA_partial_vertical_spherical_head(D, a, h)[source]¶
Calculates the partial area of a spherical tank head in the context of a vertical vessel and liquid partially filling it. This computes the wetted surface area of one of the conical heads only, and is valid for h up to a only.
- Parameters
- Returns
- SA_partial
float
Partial (wetted) surface area of one spherical tank head extending beneath the vessel, [m^2]
- SA_partial
Notes
This method is undefined for , but this is handled by returning zero.
References
- 1
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf
Examples
>>> SA_partial_vertical_spherical_head(72, a=24, h=12) 2940.5307237600464
- fluids.geometry.SA_partial_vertical_torispherical_head(D, f, k, h)[source]¶
Calculates the partial area of a torispherical tank head in the context of a vertical vessel and liquid partially filling it. This computes the wetted surface area of one of the torispherical heads only.
if :
if :
- Parameters
- D
float
Diameter of the main cylindrical section, [m]
- f
float
Dimensionless dish-radius parameter; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- k
float
Dimensionless knuckle-radius parameter; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- h
float
Height, as measured up to where the fluid ends or the top of the torispherical head, whichever is less, [m]
- D
- Returns
- SA_partial
float
Partial (wetted) surface area of one torispherical tank head, [m^2]
- SA_partial
Notes
This method is undefined for and , but those cases are handled by returning the full surface area and the zero respectively.
References
- 1
Jones, D. “Calculating Tank Wetted Area.” Text. Chemical Processing. April 2017. https://www.chemicalprocessing.com/assets/Uploads/calculating-tank-wetted-area.pdf
Examples
This method is undefined for , but this is handled by returning zero.
Miscellaneous Geometry Functions¶
- fluids.geometry.pitch_angle_solver(angle=None, pitch=None, pitch_parallel=None, pitch_normal=None)[source]¶
Utility to take any two of angle, pitch, pitch_parallel, and pitch_normal and calculate the other two. This is useful for applications with tube banks, as in shell and tube heat exchangers or air coolers and allows for a wider range of user input.
- Parameters
- angle
float
,optional
The angle of the tube layout, [degrees]
- pitch
float
,optional
The shortest distance between tube centers; defined in relation to the flow direction only, [m]
- pitch_parallel
float
,optional
The distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]
- pitch_normal
float
,optional
The distance between tube centers in a line 90° to the line of flow; has been called the transverse pitch, pn, s1, ST, and p1, [m]
- angle
- Returns
- angle
float
The angle of the tube layout, [degrees]
- pitch
float
The shortest distance between tube centers; defined in relation to the flow direction only, [m]
- pitch_parallel
float
The distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]
- pitch_normal
float
The distance between tube centers in a line 90° to the line of flow; has been called the transverse pitch, pn, s1, ST, and p1, [m]
- angle
Notes
For the 90 and 0 degree case, the normal or parallel pitches can be zero; given the angle and the zero value, obviously is it not possible to calculate the pitch and a math error will be raised.
No exception will be raised if three or four inputs are provided; the other two will simply be calculated according to the list of if statements used.
An exception will be raised if only one input is provided.
References
- 1
Schlunder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1983.
Examples
>>> pitch_angle_solver(pitch=1, angle=30) (30, 1, 0.8660254037844387, 0.49999999999999994)
- fluids.geometry.plate_enlargement_factor(amplitude, wavelength)[source]¶
Calculates the enhancement factor of the sinusoidal waves of the plate heat exchanger. This is the multiplier for the flat plate area to obtain the actual area available for heat transfer. Obtained from the following integral:
The solution to the integral is:
where E is the complete elliptic integral of the second kind, calculated with SciPy.
- Parameters
- Returns
- plate_enlargement_factor
float
The extra surface area multiplier as compared to a flat plate caused the corrugations, [-]
- plate_enlargement_factor
Notes
This is the exact analytical integral, obtained via Mathematica, Maple, and quite a bit of trial and error. It is confirmed via numerical integration. The expression normally given is an approximation as follows:
Most plate heat exchangers approximate a sinusoidal geometry only.
Examples
>>> plate_enlargement_factor(amplitude=5E-4, wavelength=3.7E-3) 1.1611862034509677
- fluids.geometry.a_torispherical(D, f, k)[source]¶
Calculates depth of a torispherical head according to [1].
- Parameters
- D
float
Diameter of the main cylindrical section, [m]
- f
float
Dimensionless dish-radius parameter; also commonly given as the product of f and D (fD), which is called dish radius and has units of length, [-]
- k
float
Dimensionless knuckle-radius parameter; also commonly given as the product of k and D (kD), which is called the knuckle radius and has units of length, [-]
- D
- Returns
- a
float
Depth of head [m]
- a
References
- 1(1,2)
Jones, D. “Calculating Tank Volume.” Text. Accessed December 22, 2015. http://www.webcalc.com.br/blog/Tank_Volume.PDF
Examples
Example from [1].
>>> a_torispherical(D=96., f=0.9, k=0.2) 25.684268924767125
- fluids.geometry.A_partial_circle(D, h)[source]¶
Calculates the partial area of a circle, in the context of the circle being an end cap to a horizontal cylindrical vessel and liquid partially filling it. This computes the wetted surface area of one of the end caps.
Multiply this by two to obtain the wetted area of two end caps.
- Parameters
- Returns
- SA_partial
float
Partial (wetted) surface area, [m^2]
- SA_partial
Notes
This method is undefined for and , but those cases are handled by returning the full surface area and the zero respectively.
References
- 1
Weisstein, Eric W. “Circular Segment.” Text. Wolfram Research, Inc. Accessed May 10, 2020. https://mathworld.wolfram.com/CircularSegment.html.
Examples
>>> A_partial_circle(D=96., h=22.0) 1251.2018147383194
- fluids.geometry.circle_segment_h_from_A(A, D)[source]¶
Calculates the height of a chord of a circle given the area of that circle segment. This is a numerical problem, solving the following equation for h.
- Parameters
- Returns
- h
float
Height measured from bottom of circle to the end of the circle section, [m]
- h
References
- 1
Weisstein, Eric W. “Circular Segment.” Text. Wolfram Research, Inc. Accessed May 10, 2020. https://mathworld.wolfram.com/CircularSegment.html.
Examples
>>> circle_segment_h_from_A(A=1251.2018147383194, D=96.) 22.0
Pellet Properties¶
- fluids.geometry.sphericity(A, V)[source]¶
Returns the sphericity of a particle of surface area A and volume V. Sphericity is the ratio of the surface area of a sphere with the same volume as the particle (equivalent diameter) to the actual surface area of the particle.
- Parameters
- Returns
- Psi
float
Sphericity [-]
- Psi
Notes
All non-spherical particles have spericities less than 1 but greater than 0. Many common geometrical shapes have their results calculated exactly in [2].
References
- 1
Rhodes, Martin J., ed. Introduction to Particle Technology. 2E. Chichester, England ; Hoboken, NJ: Wiley, 2008.
- 2
“Sphericity.” Wikipedia, March 8, 2017. https://en.wikipedia.org/w/index.php?title=Sphericity&oldid=769183043
Examples
>>> sphericity(10., 2.) 0.767663317071005
For a cube of side length a=3, the surface area is 6*a^2=54 and volume a^3=27. Its sphericity is then:
>>> sphericity(A=54, V=27) 0.8059959770082346
- fluids.geometry.aspect_ratio(Dmin, Dmax)[source]¶
Returns the aspect ratio of a shape with minimum and maximum dimension, Dmin and Dmax.
- Parameters
- Returns
- a_r
float
Aspect ratio [-]
- a_r
Examples
>>> aspect_ratio(.2, 2) 0.1
- fluids.geometry.circularity(A, P)[source]¶
Returns the circularity of a shape with area A and perimeter P.
Defined to be 1 for a circle. Used to characterize particles. Any non-circular shape must have a circularity less than one.
- Parameters
- Returns
- f_circ
float
Circularity of the shape [-]
- f_circ
Examples
Square, side length = 2 (all squares are the same):
>>> circularity(A=(2*2), P=4*2) 0.7853981633974483
Rectangle, one side length = 1, second side length = 100
>>> D1 = 1 >>> D2 = 100 >>> A = D1*D2 >>> P = 2*D1 + 2*D2 >>> circularity(A, P) 0.030796908671598795
- fluids.geometry.A_cylinder(D, L)[source]¶
Returns the surface area of a cylinder.
- Parameters
- Returns
- A
float
Surface area [m^2]
- A
Examples
>>> A_cylinder(0.01, .1) 0.0032986722862692833
- fluids.geometry.V_cylinder(D, L)[source]¶
Returns the volume of a cylinder.
- Parameters
- Returns
- V
float
Volume [m^3]
- V
Examples
>>> V_cylinder(0.01, .1) 7.853981633974484e-06
- fluids.geometry.A_hollow_cylinder(Di, Do, L)[source]¶
Returns the surface area of a hollow cylinder.
- Parameters
- Returns
- A
float
Surface area [m^2]
- A
Examples
>>> A_hollow_cylinder(0.005, 0.01, 0.1) 0.004830198704894308
- fluids.geometry.V_hollow_cylinder(Di, Do, L)[source]¶
Returns the volume of a hollow cylinder.
- Parameters
- Returns
- V
float
Volume [m^3]
- V
Examples
>>> V_hollow_cylinder(0.005, 0.01, 0.1) 5.890486225480862e-06
- fluids.geometry.A_multiple_hole_cylinder(Do, L, holes)[source]¶
Returns the surface area of a cylinder with multiple holes. Calculation will naively return a negative value or other impossible result if the number of cylinders added is physically impossible. Holes may be of different shapes, but must be perpendicular to the axis of the cylinder.
- Parameters
- Returns
- A
float
Surface area [m^2]
- A
Examples
>>> A_multiple_hole_cylinder(0.01, 0.1, [(0.005, 1)]) 0.004830198704894308
- fluids.geometry.V_multiple_hole_cylinder(Do, L, holes)[source]¶
Returns the solid volume of a cylinder with multiple cylindrical holes. Calculation will naively return a negative value or other impossible result if the number of cylinders added is physically impossible.
- Parameters
- Returns
- V
float
Volume [m^3]
- V
Examples
>>> V_multiple_hole_cylinder(0.01, 0.1, [(0.005, 1)]) 5.890486225480862e-06