Change in height

2.7

m

Outlet pipe diameter

5

cm

Inlet pressure

100

kPa

Inlet velocity

1.0

m/s

Display:

This application simulates water flowing through a pipe with an inlet diameter of 5 cm. You can adjust the outlet height (i.e., change Δz), outlet pipe diameter, inlet gauge pressure, and inlet velocity using the sliders. You can toggle which variables are displayed by pressing "Fluid properties" or "Energy". The outlet conditions are calculated using Bernoulli's equation. To learn more about Bernoulli's equation, click the "Details" button.

Bernoulli's equation is a steady-state energy balance. It states that the sum of a fluid's kinetic energy, potential energy and pressure are constant along a streamline. For incompressible flow, Bernoulli's equation is: $$ \frac{ \rho u^{2} }{ 2 } + \rho gz + P = constant $$ where \( u \) is fluid velocity, \( g \) is the gravitational constant (9.81 m/s^{2}), \( P \) is pressure, and \( \rho \) is fluid density. Thus, the properties at the outlet can be determined given the properties at the inlet: $$ \frac{ \rho u^{2}_{in} }{ 2 } + \rho gz_{in} + P_{in} = \frac{ \rho u^{2}_{out} }{ 2 } + \rho gz_{out} + P_{out} $$ A mass balance is required to solve for \( u_{out} \). The volumetric flowrate is constant because the fluid is assumed to be incompressible, meaning velocity times cross-sectional area remains constant: $$ \frac{ \pi D_{ in }^{ 2 } }{4} u_{in} = \frac{ \pi D_{ out }^{ 2 } }{4} u_{out} $$ where \( D_{i} \) is pipe diameter. Solving for the fluid velocity at the outlet, $$ u_{out} = u_{in} \frac{ D^{2}_{in} }{ D^{2}_{out} } $$

This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Neil Hendren under the direction of Professor John L. Falconer. This simulation was prepared with financial support from the National Science Foundation. Address any questions or comments to learncheme@gmail.com. All of our simulations are open source, and are available on our LearnChemE Github repository.

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