Water flows through a horizontal pipe of varying cross-section at a rate of 0.314 ~m^3 ~s^-1 . The velocity of water at a point where the radius of the pipe is 10 cm is

Correct answer: (C) 10 ~ms^-1. Given, flow rate, Q=0.314 ~m^3 ~s^-1 r=10 ~cm=0.1 ~m =10^-1 ~m Since, Q=A v 0.314=π r^2 v 0.314=314 × 10^-2 v ⇒ v=10 ~m / s

Q178 / 180 · KCET 2024 · Physics

Water flows through a horizontal pipe of varying cross-section at a rate of $0.314 \mathrm{~m}^3 \mathrm{~s}^{-1}$. The velocity of water at a point where the radius of the pipe is 10 cm is

A
$0.1 \mathrm{~ms}^{-1}$
B
$1 \mathrm{~ms}^{-1}$
Correct answer
C
$10 \mathrm{~ms}^{-1}$
D
$100 \mathrm{~ms}^{-1}$

Solution

Given, flow rate, $Q=0.314 \mathrm{~m}^3 \mathrm{~s}^{-1}$ $r=10 \mathrm{~cm}=0.1 \mathrm{~m}$ $=10^{-1} \mathrm{~m}$ Since, $\quad Q=A v$ $0.314=\pi r^2 v$ $0.314=314 \times 10^{-2} v$ $\Rightarrow \quad v=10 \mathrm{~m} / \mathrm{s}$

Hence, the correct answer is option: 'C'.

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