# Pump system with dynamic head

Given:

• A pump system is defined with dynamic head of 46 feet.
• The height between the static pressure gauge and the surface of the water is 9 feet.

Assumptions:

• Friction losses between the tank and pump are approximately 0.

Hint:

• The pressure gauge is capable of sensing static head, but not velocity head.

Find:

• The velocity of the water through the pipe.

Work:

Use Bernoulli's equation, solve for V2.

$$\dfrac{P_1 * g_c}{\rho g} + \dfrac{v_1^2}{2 g} + Z_1 = \dfrac{P_2 * g_c}{\rho g} + \dfrac{v_2^2}{2 g} + Z_2 + H_A$$

Rearrange to solve for V2. $$v_2 = [(\dfrac{(P1 - P2)g_c}{\rho g} + Z_1 - Z_2 - H_A)2 g]^{1/2}$$

Point 1 is defined at surface of water...

$$v_1(@P_1) = 0 ft/sec, Z_1(@P_1) = 9 ft, P_1(@P_1) = 0 PSIG.$$

Point 2 is defined at static pressure gauge...

$$P_2(@P_2) = 23 PSIG, Z_2(@P_2) = 0 ft.$$

$$v_2 = [(\dfrac{(P1 - P2)g_c}{\rho g} + Z_1 - H_A)2 g]^{1/2}$$

Should the dynamic head $$H_A$$ be added or subtracted here?

• Thanks, I modified the question. This is not a homework problem. It is a diagnostic test problem for the ME PE exam. – Jason Feb 23 at 19:22