# 7.10 Piping Systems - Steam

40 bar steam, 450 degrees Celsius flows though a 120 m long horizontal 150mm schedule 80 pipe at a rate of 40000 kg/hr.

There are three 90 degree weld elbows with rc=1.5, 1 fully open class 600 150mm x 100mm venturi class gate valve, one class 600 150 mm class y pattern globe valve with a seat diameter of 90% the inside pipe diameter (disc fully lifted).

Calculate the pressure drop through the system.

    [1]:

    from math import *
    from fluids.units import *
    from thermo.units import Stream

    m = 40000*u.kg/u.hr
    T = 450*u.degC
    P = 40*u.bar

    steam = Stream('water', T=T, P=P, m=m)

    rho = steam.rho
    mu = steam.mu
    print('Density = %s' %rho)
    print('Viscosity = %s' %mu)

    Density = 11.98501086830739 kilogram / meter ** 3
    Viscosity = 2.6514617050585646e-05 pascal * second

    [2]:

    L = 120*u.m
    NPS, D_pipe, Do_pipe, t = nearest_pipe(Do=150*u.mm, schedule='80')
    Q = m/rho
    v = Q/(pi/4*D_pipe**2)
    Re = Reynolds(rho=rho, mu=mu, D=D_pipe, V=v)
    fd = friction_factor(Re=Re, eD=0.0018*u.inch/D_pipe)
    K_elbow = bend_rounded(Di=D_pipe, angle=90*u.degrees, fd=fd, bend_diameters=1.5)
    K_friction = K_from_f(fd=fd, L=L, D=D_pipe)
    K_globe_valve = K_globe_valve_Crane(D1=0.9*D_pipe, D2=D_pipe, fd=fd)
    # Angle and inside diameter are taken from example 7.4,
    K_gate_valve = K_gate_valve_Crane(D1=100*u.mm, D2=D_pipe, angle=13.115*u.degrees, fd=fd)

    K_tot = K_gate_valve + K_globe_valve + 3*K_elbow + K_friction
    dP = dP_from_K(K=K_tot, rho=rho, V=v)

    print('Crane elbow term = 0.63; calculated = %s' % (3*K_elbow))
    print('Crane globe valve term = 1.44; calculated = %s' % (K_globe_valve))
    print('Crane gate valve term = 1.22; calculated = %s' % (K_gate_valve))
    print('Crane friction term = 12.3; calculated = %s' % (K_friction))
    print('Darcy friction factor = %s' %fd)
    print('Pressure drop = %s' %dP.to(u.Pa))

    Crane elbow term = 0.63; calculated = 0.6059161440546141 dimensionless
    Crane globe valve term = 1.44; calculated = 7.971314885893429 dimensionless
    Crane gate valve term = 1.22; calculated = 1.171521564942793 dimensionless
    Crane friction term = 12.3; calculated = 12.522683061833051 dimensionless
    Darcy friction factor = 0.015273499107749047 dimensionless
    Pressure drop = 405252.2181183786 pascal

This compares terribly to the example, which calculates a pressure drop of 274800 Pa!

Two errors are apparent - their example uses a different coefficient (55) in the globe valve pressure drop equation than that shown in their appendix (340); and they re-use their prior calculated gate valve, despite the friction factor being different in this example. This, plus their use of a constant 0.015 friction factor, explains the difference.

The example below uses their calculated globe valve pressure drop and their friction factor. The result (268500 Pa) compares well with their calculation; the additional decimals and better physical properties explain the rest.

    [3]:

    L = 120*u.m
    NPS, D_pipe, Do_pipe, t = nearest_pipe(Do=150*u.mm, schedule='80')
    Q = m/rho
    v = Q/(pi/4*D_pipe**2)
    Re = Reynolds(rho=rho, mu=mu, D=D_pipe, V=v)
    fd = 0.015
    K_elbow = bend_rounded(Di=D_pipe, angle=90*u.degrees, fd=fd, bend_diameters=1.5)
    K_friction = K_from_f(fd=fd, L=L, D=D_pipe)
    K_globe_valve = 1.44
    # Angle and inside diameter are taken from example 7.4,
    K_gate_valve = K_gate_valve_Crane(D1=100*u.mm, D2=D_pipe, angle=13.115*u.degrees, fd=fd)

    K_tot = K_gate_valve + K_globe_valve + 3*K_elbow + K_friction
    dP = dP_from_K(K=K_tot, rho=rho, V=v)

    print('Crane elbow term = 0.63; calculated = %s' % (3*K_elbow))
    print('Crane globe valve term = 1.44; calculated = %s' % (K_globe_valve))
    print('Crane gate valve term = 1.22; calculated = %s' % (K_gate_valve))
    print('Crane friction term = 12.3; calculated = %s' % (K_friction))
    print('Darcy friction factor = %s' %fd)
    print('Pressure drop = %s' %dP.to(u.Pa))

    Crane elbow term = 0.63; calculated = 0.5988647407128814 dimensionless
    Crane globe valve term = 1.44; calculated = 1.44
    Crane gate valve term = 1.22; calculated = 1.1614815235317342 dimensionless
    Crane friction term = 12.3; calculated = 12.29844219732167 dimensionless
    Darcy friction factor = 0.015
    Pressure drop = 282016.77247066115 pascal