Pump system with dynamic head

Question

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?