7.29 Orifice Flow Rate Calculation

Given a differential pressure of 17 kPa is measured across taps located 1D upstream/0.5D downstream from the inlet face of a 50 mm ID orifice plate in an 80 mm schedule 80 steel pipe carrying water 15 deg C. Find the flow rate in gallons/minute.

from fluids.units import *
from thermo.units import Chemical

P1 = 2*u.bar # The full set of equations requires actual pressures not just the pressure difference, so an initial pressure of 2 bar is assumed.
P2 = P1 -  17*u.kPa
taps = 'D'
meter_type = 'ISO 5167 orifice'
Do = 50*u.mm

NPS, D, _, t_pipe = nearest_pipe(Do=80*u.mm, schedule=80)

D

0.07366 meter

water = Chemical('water', T=15*u.degC, P=P1)
rho = water.rho
mu = water.mu
k = water.isentropic_exponent
rho, mu, k

(999.149354395164 <Unit('kilogram / meter ** 3')>,
 0.0011375132802133906 <Unit('pascal * second')>,
 1.329536639348325 <Unit('dimensionless')>)

m = differential_pressure_meter_solver(D=D, D2=Do, P1=P1, P2=P2, rho=rho, mu=mu, k=k, meter_type=meter_type, taps=taps)
print(m)
Q = m/rho
print(Q.to('L/min'))

7.704278611291563 kilogram / second
462.6502680946246 liter / minute

The answer given in TP410M is 478 gallons/minute; however the errata specifies this value is in units of liters/minute instead.

This calculation matches their result well, given they did not include expansivity in their calculations and read a value of C from a graph.

A calculator at flow of fluids, which also does not include expansivity, gives an answer of 476.777 L/min, along with 7.93916 kg/s (http://www.flowoffluids.com/calculators/flow-through-orifices.aspx).