JEE Main 2023PhysicsMechanical Properties of FluidsEasyNumerical

JEE Main 2023 — Mechanical Properties of Fluids Question with Solution

JEE Main 2023 (12 Apr Shift 1)

Question

Glycerin of density 1.25×103 kg m–3 is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends are 10 cm2 and 5 cm2 and pressure drop across its length is 3 N m–2. The rate of flow of glycerine through the pipe is x×10–5 m3 s–1. The value of x is _____.

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Show full solutionCorrect answer: 4
Correct answer
4

Step-by-step explanation

It is given that

A1=10 cm2; A2=5 cm2

∆P=3 N m-2

By continuity equation,

A1v1=A2v2⇒v1=A2v2A1   ...(i)

By Bernoulli's equation,

12ρv22-12ρv12=∆P   ...(ii)

Using equation (i) in (ii)

∆P=ρ2(v22-A2v2A12)⇒∆P=ρv2221-A2A12⇒3=1.25×103×v2221-14⇒v22=6×41.25×103×3⇒v2=8×10-2 m s-1

So, the discharge rate is,

A2v2=x×10-5⇒x=5×10-4×8×10-210-5=4

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About this question

This is a previous-year question from JEE Main 2023, covering the Mechanical Properties of Fluids chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.