---
title: "Types of heads and Bernoulli's assumptions"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:heads-bernoulli-assumptions"
source: https://www.bctengineer.com/q/semester_6/hydro_power/heads-bernoulli-assumptions
site: BCT Engineering
---

# Types of heads and Bernoulli's assumptions

Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics

- Asked in: 2082 Kartik, 3+1+2 marks; 2071 Magh, 2+3 marks (asked 2 times)
- Video: [Understanding Bernoulli's Equation](https://www.youtube.com/watch?v=DW4rItB20h4) — The Efficient Engineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/heads-bernoulli-assumptions
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Briefly explain the different types of heads in a moving liquid. Define Bernoulli's equation and list the assumptions made in its derivation.

## Short answer

Heads are pressure head p/ρg, velocity head V^2/2g, and potential head z. Bernoulli's equation: p/ρg + V^2/2g + z = constant along a streamline for steady, incompressible, ideal flow with no energy added or removed. Assumptions: ideal fluid, steady, incompressible, irrotational, uniform velocity, no pump/turbine.

## Answer

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).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which pair correctly names the heads in Bernoulli's equation?
   A. Pressure head p/rho g, velocity head V^2/2g, potential head z
   B. Pressure head V^2/2g, velocity head p/rho g, potential head z
   C. Pressure head p/rho, velocity head V/2g, potential head z
   D. Pressure head p g, velocity head V^2, potential head rho z
   Answer: A. Pressure head is p/rho g, velocity head is V^2/2g and potential head is z above the datum. (Key point: Types of head)

2. What does Bernoulli's equation state?
   A. Velocity is constant along a streamline
   B. For steady, ideal, incompressible flow along a streamline the total head is constant
   C. Pressure is constant in a moving fluid
   D. Total head always decreases along a streamline
   Answer: B. p/rho g + V^2/2g + z = constant along a streamline under the stated assumptions. (Key point: Bernoulli statement)

3. Which is NOT an assumption in deriving Bernoulli's equation?
   A. Flow is steady
   B. Fluid is incompressible
   C. Fluid is ideal (non-viscous)
   D. Energy is added by a pump along the path
   Answer: D. No energy may be added or removed (no pump or turbine) and no heat transfer is assumed. (Key point: Assumptions)

4. Total head H and piezometric head are:
   A. H = p/rho g + z; piezometric = p/rho g + V^2/2g + z
   B. H = p/rho g + V^2/2g + z; piezometric = p/rho g + z
   C. Both equal p/rho g + z
   D. Both equal V^2/2g + z
   Answer: B. Total head includes velocity head (energy line); piezometric head excludes it (hydraulic grade line). (Key point: Piezometric and total head)

## Related in Hydro Power

- [Bernoulli's equation in real practice](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Abernoulli-real-practice) — Hydro Power, chapter 1
- [Deriving Bernoulli's equation from Euler's equation](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aeuler-bernoulli-derivation) — Hydro Power, chapter 1
- [Bernoulli's equation limitations and application](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Abernoulli-limitations-application) — Hydro Power, chapter 1
- [Continuity equation basis and Bernoulli equation](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Acontinuity-and-bernoulli) — Hydro Power, chapter 1
- [Bernoulli for real flow with HGL and EGL](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Abernoulli-real-flow-hgl-egl) — Hydro Power, chapter 1

## Related in other subjects

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