Fluid Flow

Calculate the pressure drop in a length of pipe

Fluid Properties

Piping Properties

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Answer

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Governing Equation

The Bernoulli Equation is used to determine pressure drop

P1+ρgh1+12ρv12=P2+ρgh2+12ρv22+(fdLdi+∑K)12ρv2P_{1} + {\rho}gh_{1} + \frac{1}{2}{\rho}v_{1}^{2} = P_{2} + {\rho}gh_{2} + \frac{1}{2}{\rho}v_{2}^{2} + \left ( {f_{d}\frac{L}{d_i}} + \sum K \right )\frac{1}{2}{\rho}{v}^{2}

With the following assumptions:

  • The start and end are connected through a fluid streamline
  • The fluid has constant density
  • The fluid flow rate is constant

Rearrage to solve for pressure drop:

P1−P2=ρg(h2−h1)+12ρ(v22−v12)+(fdLdi+∑K)12ρv2P_{1} - P_{2} = {\rho}g \left (h_{2}-h_{1}\right ) + \frac{1}{2}{\rho} \left ( v_{2}^{2} - v_{1}^{2} \right ) + \left ( {f_{d}\frac{L}{d_i}} + \sum K \right )\frac{1}{2}{\rho}v^{2}

Simplify:

P1−P2=ΔPP_{1} - P_{2} = \Delta P
h2−h1=Δhh_{2} - h_{1} = \Delta h
v22−v12=0v_{2}^{2} - v_{1}^{2} = 0
ΔP=ρgΔh+(fdLdi+∑K)12ρv2\Delta P = {\rho}g\Delta h + \left ( {f_d\frac{L}{d_i}} + \sum K \right )\frac{1}{2}{\rho}v^{2}

Definitions

P=P =
Pressure
v=v =
Fluid velocity
ρ=\rho =
Fluid density
di=d_i =
Inner pipe diameter
L=L =
Pipe length
h=h =
Elevation
ϵ=\epsilon =
Surface roughness
fd=f_d =
Darcy friction factor
K=K =
Loss coefficient