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# Triangular Notch

Discharge over a Triangular Notch
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### 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 triangular notch is also called a V-notch. Consider a triangular notch, in one side of the tank, over which water is flowing as shown in figure.

Let,
• H = Height of the liquid above the apex of the notch
• θ = Angle of the notch
• Cd = Coefficient of discharge

From the geometry of the figure, we find that the width of the notch at the water surface,

Area of the strip =

We know that the theoretical velocity of water through the strip =

and discharge over the notch,

The total discharge over the whole notch may be found out only by integrating the above equation within the limits 0 and H.

A triangular notch gives more accurate results for low discharges than rectangular notch and the same triangular notch can measure a wide range of flows accurately.

Example:

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##### Example - Discharge through a triangular notch
Problem
A right-angled V-notch was used to measure the discharge of a centrifugal pump. If the depth of water at V-notch is 200mm, calculate the discharge over the notch in liters per minute. Assume coefficient of discharge as 0.62.
Workings
Given,

We know that the discharge over the triangular notch,

Solution
Discharge over the notch = 1560 liters/s