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# Stepped Notch

Discharge over a Stepped Notch View version details

### 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,
• H1 = Height of the liquid above the sill of notch 1
• b1 = Breadth of notch 1
• H2, b2 = Corresponding values for notch 2, and
• Cd = Coefficient of discharge for both the notches

From the geometry of the notch, we get, and the discharge over the notch 2, Now the total discharge over the notch, Example:
[metric]
##### Example - Discharge over a Stepped Notch
Problem
Find the discharge in m3 /s over a stepped notch shown in figure. The level of water coincides with the top of the notch. Take Cd for all sections 0.6. All dimensions are in mm.
Workings
Given,
• Cd = 0.6

We know that the total discharge over the stepped notch,

Solution
Discharge over the notch = 0.779 m3 /s