WikiEngineer :: Water-Resources :: Bernoulli Equation

Assumptions when using Bernoulli's Equation:

Bernoulli's equation assumes the following are true:

There is no fluid friction.
Changes in thermal energy is negligible (the fluid is adiabatic).
The fluid is incompressible.
The fluid is inviscid.
Steady state flow exists.
Flow is a streamline.

Using Bernoulli's:

Bernoulli's equation is an energy conservation equation that will work for vapors, gasses, and fluids (both laminar and turbulent). This is assuming that all the assumptions have been met.

Below is many different variations of the general equation. The main difference between US and SI is the US units already have gravity incorporated into them.

where:

Z_1/2 = The static head or elevation (in feet or meters) above a datum
P_1/2 = The pressure of pipe at a given location
V_1/2 = The velocity of the fluid at a given location
ρ = the density of the fluid/vapor/gas being used
g = acceleration of gravity
h_L = the head loss the system will experience between points 1 and 2 along a pipe. See Minor Losses.

Bernoulli's Equations for both US and SI units:
General Equation (US):

{Z_1}+{P_1\over{ρg}}+{V^2_1\over{2g}}= {Z_2}+{P_2\over{ρg}}+{V^2_2\over{2g}}+h_L

General Equation (SI):

{Z_1*g}+{P_1\over{ρ}}+{V^2_1\over{2}}= {Z_2*g}+{P_2\over{ρ}}+{V^2_2\over{2}}+h_L

Solve for Head Loss (US):

h_L = {Z_1-Z_2+{P_1-P_2\over{ρg}}+{V^2_1-V^2_2\over{2g}}}

Solve for Static Head or Elevation (US):

Z_1 = {Z_2+{P_2-P_1\over{ρg}}+{V^2_2-V^2_1\over{2g}}+h_L}

Solve for the Pressure at Point 1 (US):

P_1 = ρg\left({Z_2-Z_1+{P_2\over{ρg}}+{V^2_2-V^2_1\over{2g}}+h_L}\right)

Solve for the Velocity at Point 1 (US):

V_1 = \sqrt{2g\left({Z_2-Z_1+{P_2-P_1\over{ρg}}+{V^2_2\over{2g}}+h_L}\right)}

References:

P. Aarne Vesilind, J. Jeffrey Peirce and Ruth F. Weiner. 1994. Environmental Engineering. Butterworth Heinemann. 3rd ed.