Q130 / 180 · KCET 2025 · Physics

A horizontal pipe carries water in a streamlined flow. At a point along the pipe, where the cross-sectional area is $10 \mathrm{~cm}^{-2}$, the velocity of water is $1 \mathrm{~ms}^{-1}$ and the pressure is 2000 Pa . What is the pressure of water at another point where the cross-sectional area is $5 \mathrm{~cm}^2$ ? [Density of water $=1000 \mathrm{kgm}^{-3}$ ]

  • A
    300 Pa
  • B
    400 Pa
  • Correct answer
    C
    500 Pa
  • D
    200 Pa

Solution

$\begin{aligned} & A_2 V_2=A_1 V_1 \quad \therefore V_2=\frac{A_1 V_1}{A_2}=\frac{10 \times 1}{5}=2 \mathrm{~m} / \mathrm{s} \\ & P_2+\frac{1}{2} P V_2^2=P_1+\frac{1}{2} P V_1^2 \\ & P_2=2000+\frac{1}{2} \times 1000 \times\left(1^2-2^2\right)=500 \mathrm{~Pa}\end{aligned}$

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

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