Archived Fluid Mechanics - Piezometric Head

[VitaX]

Homework Statement

Homework Equations

Provided above

The Attempt at a Solution

Piezometric head is defined as the pressure head plus the elevation head, correct? But how does having a high piezometric head tell you about the fluid flow?

Since the diameters are equal, the area's are equal, hence velocities are equal. But how do I show the direction of flow without putting in any numerical values?

 

[MexChemE]

First, let's assume point 1 is upstream from point 2. It makes sense that way, as the head gain from the pump (h_p) appears in the LHS of the equation, and the head losses from the turbine and due to friction appear in the RHS. They can be thought of as inputs and outputs in an energy balance, well, that is exactly what the equation is. There are no pumps or turbines in the system and the diameter is constant, so
h_p = 0
h_t = 0
V_1 = V_2
Now, the energy equation is reduced to
\left( \frac{p_1}{\gamma} + z_1 \right) - \left( \frac{p_2}{\gamma} + z_2 \right) = h_L
Piezometric head is defined as
h = \frac{p}{\gamma} + z
So we have
h_1 - h_2 = h_L
Now, head loss is always a positive number, therefore
h_1 > h_2
So the fluid flows from the point with higher piezometric head to the point with lower piezometric head.