z in incompressible flow equation

Question

I'm trying to calculate the flow rate out of my water tank.

On Wikipedia one can find Bernoulli's incompressible flow equation as: $$\frac{v^2}2 + gz + \frac p \rho = \mathrm{const}$$

With $p = \rho g h$ for hydrostatic pressure this yields:

$$v = \sqrt{2(\mathrm{const} - g(z + h))}$$

I understand that v is the flow speed and that h is the height difference between the water level in the tank and the outflow.

Two questions:

1. The variable $z$ is described as "elevation of the point above a reference plane". How is this reference plane to be chosen?

2. What does $\mathrm{const}$ depend on and how can it be determined?

Answer 1

You can choose any vertical reference point. Changing the point of vertical reference (your vertical datum) just changes the value of the constant

You evaluate the equation at any two points, and then set the two left hand sides equal to each other. This gives a relationship between the pressure, velocity, and height at two different points. The constant goes away.

By choosing your value of Z wisely, you can make things simple.

Since the equation is linear in pressure (P), you can also choose your pressure reference (your pressure datum), and the equation is still valid. Engineers use gage pressure, which is the difference from the atmospheric pressure. This way, the pressure at the surface exposed to air is just zero.