If the flow is critical in a channel then : (Symbols have normal meanings)

This question was previously asked in
UKPSC JE Civil 8 May 2022 Official Paper-II
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  1. Q2T = gA3
  2. QT2 = gA2

Answer (Detailed Solution Below)

Option 3 : Q2T = gA3
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UKPSC JE CE Full Test 1 (Paper I)
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Detailed Solution

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Concept:

Critical Flow:

It is defined as the flow for which the specific energy is minimum and Froude’s number is equal to unity.

Froude’s no. (Fr) = 

Where,

Inertial force = ρ × Q × v

(ρ = Density, Q = Discharge, v = velocity)

Gravity force = ρ × g × V;

(ρ = Density, g = Gravity acceleration, V = Volume)

Now,

 (∵ A = L × T, ν = Q/A)

A = Area, L = Length, and T = Top width

Now, for a critical flow Fr = 1

Q2T = gA3

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