# Stepped Notch

Discharge over a Stepped Notch

### Key Facts

**Gyroscopic Couple**: The rate of change of angular momentum () = (In the limit).

- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.

**Blaise Pascal**(1623-1662) was a French mathematician, physicist, inventor, writer and Catholic philosopher.

**Leonhard Euler**(1707-1783) was a pioneering Swiss mathematician and physicist.

## Overview

A stepped notch is a combination of rectangular notches as shown in figure. It is thus obvious that the discharge over such a notch will be the sum of the discharges over the different rectangular notches. Consider a stepped notch as shown in figure. For the purpose of analysis, let us split up the notch into two rectangular notches**1**and

**2**. The total discharge over the notch will be the sum of the discharges over the two rectangular notches. Let,

- H
_{1}= Height of the liquid above the sill of notch**1** - b
_{1}= Breadth of notch**1** - H
_{2}, b_{2}= Corresponding values for notch**2**, and - C
_{d}= Coefficient of discharge for both the notches

**2**, Now the total discharge over the notch,

Example:

[metric]

##### Example - Discharge over a Stepped Notch

Problem

Find the discharge in m

^{3}/s over a stepped notch shown in figure. The level of water coincides with the top of the notch. Take C_{d}for all sections 0.6. All dimensions are in mm.Workings

Given,

- C
_{d}= 0.6

Solution

Discharge over the notch = 0.779 m

^{3}/s