Bernoulli Equation

\[
\bigg(\frac{P_1}{\rho}\bigg)+\bigg(\frac{v_1^2}{2g}\bigg)+(Z_1) = \bigg(\frac{P_2}{\rho}\bigg)+\bigg(\frac{v_2^2}{2g}\bigg)+(Z_2)+HL\] 
where: P = fluid static pressure
ρ = fluid density
v = fluid velocity
g = gravitational constant
Z = elevation
HL = friction head losses through pipe/valves/fittings
If the two points are the inlet and outlet of a pipeline, then we can make some assumptions. The flow rate will be the same at the inlet and outlet, so the fluid velocity will be the same. These terms drop out of the equation. Then:

\[
dP = P_2P_1 = (Z_1Z_2HL)\rho\] 
Now, if the endpoints of the pipeline are the same \(
(Z_1 = Z_2)\), or if the inlet is lower than the outlet \(
(Z_1 < Z_2)\), then the dP will definitely be negative. But, if the inlet is higher than the outlet \(
(Z_1 > Z_2)\), then there is the possibility that the dP could be positive. If the drop in elevation is greater than the friction losses \(
({Z_1  Z_2} > HL)\), then the pipeline dP will be positive.
1 Comment
Jeff Sines
Reviewed