Water is flowing in streamline manner in a horizontal pipe. If the pressure at a point where cross-sectional…

Water is flowing in streamline manner in a horizontal pipe. If the pressure at a point where cross-sectional area is $10 \mathrm{~cm}^2$ and velocity $1 \mathrm{~ms}^{-1}$ is 2000 Pa , then the pressure of water at another point where the cross-sectional area $5 \mathrm{~cm}^2$ is
  1. 2500 Pa
  2. 2000 Pa
  3. 1000 Pa
  4. 500 Pa

Solution

By equation of continuity $\begin{aligned} & A_1 V_1=A_2 V_2 \\ & \Rightarrow 10 \times 1=5 v_2 \Rightarrow v_2=2 \mathrm{~m} / \mathrm{s} \end{aligned}$
Applying Bernoulli's theorem at point 1 and 2 , $\begin{aligned} & \mathrm{P}_1=\frac{1}{2} \delta \mathrm{v}_1^2=\mathrm{P}_2+\frac{1}{2} \delta \mathrm{v}_2^2 \\ & \Rightarrow 2000+\frac{1}{2} \times 10^3 \times 1^2=\mathrm{P}_2+\frac{1}{2} \times 10^3 \times 2^2 \\ & \therefore \quad \mathrm{P}_2=2000+\frac{1}{2} \times 10^3\left(1^2-2^2\right) \\ & =500 \mathrm{~Pa} \end{aligned}$

Asked in: AP EAMCET 2024 (22 May Shift 1)

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