KCET · Physics · Mechanical Properties of Fluids

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
C 500 Pa
D 200 Pa

Verified Solution

Answer & Solution

Correct Answer

(C) 500 Pa

Step-by-step Solution

Detailed explanation

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

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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