---
title: "Spillway model height, head and flow"
subject: "Fluid Mechanics"
chapter: 10
key: "semester_3/fluid_mechanics:spillway-model-height-head-flow"
source: https://www.bctengineer.com/q/semester_3/fluid_mechanics/spillway-model-height-head-flow
site: BCT Engineering
---

# Spillway model height, head and flow

Fluid Mechanics · Chapter 10: Similitude and physical modeling

- Asked in: 2075 Chaitra, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/fluid_mechanics/spillway-model-height-head-flow
- Whole chapter: https://www.bctengineer.com/md/semester_3/fluid_mechanics/chapter-10

## Question

A spillway model is to be built geometrically similar scale of 1/16 across a flume of 60 cm width. The prototype is 12.5 m high and the maximum head on it is expected to be 2 m. (i) What height of the model and what head on the model should be used? (ii) If the flow over the model at a particular head is 20 lps, what flow per m length of the prototype is expected?

## Short answer

(i) model spillway height 0.781 m, head 0.125 m. (ii) prototype flow per metre length ≈ 2133 L/s (2.13 m³/s/m).

## Answer

Spillway flow is gravity-dominated, so the Froude law is used. Length scale $L_r = L_m/L_p = 1/16$.

#### (i) Model dimensions

$$
\begin{aligned}
H_m &= \frac{12.5}{16} = 0.78125\ \text{m} \approx 0.78\ \text{m} \\
h_m &= \frac{2}{16} = 0.125\ \text{m} = 12.5\ \text{cm}
\end{aligned}
$$

#### (ii) Flow per metre length of the prototype

Model flume width $= 0.60$ m, $Q_m = 20$ L/s.

$$
q_m = \frac{20}{0.6} = 33.33\ \text{L/s per m}
$$

For Froude similarity, the discharge scale is $Q_r = L_r^{5/2}$, and the discharge per unit length scale is $q_r = L_r^{3/2}$:

$$
q_p = \frac{q_m}{L_r^{3/2}} = 33.33\times16^{3/2} = 33.33\times64 = 2133\ \text{L/s per m}
$$

**Answer: (i) model spillway height $= 0.781$ m and head $= 0.125$ m; (ii) prototype discharge $\approx 2133$ L/s per metre length $= 2.13\ \text{m}^3/\text{s}$ per m.**

## Check yourself

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

1. Which law is used for spillway flow?
   A. Reynolds law
   B. Mach law
   C. Froude law
   D. Weber law
   Answer: C. Gravity dominates spillway flow. (Key point: Governing law)

2. What is the model height?
   A. 12.5 m
   B. 0.125 m
   C. 200 m
   D. 0.781 m
   Answer: D. 12.5/16 = 0.78125 m. (Key point: Model height)

3. What is the model head?
   A. 0.125 m
   B. 0.781 m
   C. 32 m
   D. 0.5 m
   Answer: A. 2/16 = 0.125 m. (Key point: Model head)

4. What is the scale for discharge per unit length?
   A. L_r^(5/2)
   B. L_r^(3/2)
   C. L_r^(1/2)
   D. L_r^2
   Answer: B. Q_r = L_r^(5/2) divided by the length scale gives L_r^(3/2). q_p = 33.33 x 64 = 2133 L/s per m. (Key point: Discharge per metre scale)

## Related in Fluid Mechanics

- [Model time scale, prototype day and moon](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Amodel-time-scale-moon-gravity) — Fluid Mechanics, chapter 10
- [Model velocity and flow for oil pipeline (0.042 poise)](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Apipeline-oil-model-water-0042) — Fluid Mechanics, chapter 10
- [Model velocity and flow for oil pipeline (0.04 poise)](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Apipeline-oil-model-water-004) — Fluid Mechanics, chapter 10
- [Model liquid viscosity, Froude and Reynolds](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Amodel-liquid-viscosity-froude-reynolds) — Fluid Mechanics, chapter 10
- [Rotating tube with quadrant, speed and head](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Arotating-tube-abcd-speed) — Fluid Mechanics, chapter 2
- [Orifice plate flow in hydropower canal](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aorifice-plate-canal-flow) — Fluid Mechanics, chapter 6

## Related in other subjects

- [Similitude and scale model of a bracket](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Asimilitude-scale-model-cantilever) — Machine Design II, chapter 1
- [Froude model of a spillway](https://www.bctengineer.com/question.md?key=semester_4%2Ffluid_mechanics_mechanical%3Aspillway-model-froude-scaling) — Fluid Mechanics, chapter 5
- [Flying height from photo and map scale](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aflying-height-pq-20cm-focal-24) — Surveying II, chapter 7
- [Prototype model and when to use it](https://www.bctengineer.com/question.md?key=semester_5%2Fsoftware_engineering%3Aprototype-model) — Software Engineering, chapter 1