Types of heads and Bernoulli's assumptions

In a moving liquid the energy per unit weight is called head (unit m). There are three main heads.

Types of heads

1. Pressure head, $p/\rho g$: energy due to pressure; the height of liquid column the pressure can support.
2. Velocity (kinetic) head, $V^2/2g$: energy due to motion; the height a particle would rise if its velocity were turned upwards.
3. Potential (datum) head, $z$: energy due to position above an arbitrary datum.

• Piezometric head $= p/\rho g + z$ (level shown by a piezometer, defines the HGL).
• Total head $H = p/\rho g + V^2/2g + z$ (defines the energy line). In real flows a loss of head $h_L$ due to friction and fittings also appears.

Bernoulli's equation

For steady, ideal, incompressible flow along a streamline, the total head is constant:

$$\frac{p}{\rho g} + \frac{V^2}{2g} + z = \text{constant}$$

or between sections 1 and 2:

$$\frac{p_1}{\rho g} + \frac{V_1^2}{2g} + z_1 = \frac{p_2}{\rho g} + \frac{V_2^2}{2g} + z_2$$

Assumptions

1. The fluid is ideal (non-viscous), so there is no friction loss.
2. The flow is steady.
3. The flow is incompressible ($\rho$ constant).
4. The flow is irrotational and the equation is applied along a streamline.
5. Only gravity and pressure forces act; no energy is added or removed (no pump or turbine) and no heat transfer.
6. Velocity is uniform over the section (one-dimensional flow).