एक द्रव जिसका घनत्व \(750\,kgm ^{-3}\) है, एक चिकनी क्षैतिज पाइप में बह रहा है। यदि पाईप का अनुप्रस्थ काट \(A _1=1.2 \times 10^{-2}\,m ^2\) से \(A _2=\frac{ A _1}{2}\) तक बदले तथा चौड़े तथा सकड़े भागों के मध्य दाबान्तर \(4500\,Pa\) है, तो द्रव के प्रवाह की दर \(............ \times 10^{-3} m ^3 s ^{-1}\) ज्ञात कीजिये।

A \(20\)
B \(23\)
C \(24\)
D \(29\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(24\)

Step-by-step Solution

Detailed explanation

\(A _{2}=\frac{ A _{1}}{2}\) \(P _{1}- P _{2}=4500\,Pa\) \(P _{1}+\frac{1}{2} \rho V _{1}^{2}+\rho gh = P _{2}+\frac{1}{2} \rho V _{2}^{2}+\rho gh\) \(P _{1}- P _{2}=\frac{1}{2} \rho\left( V _{2}^{2}- V _{1}^{2}\right)\) And \(A _{1} V _{1}= A _{2} V _{2}\)…

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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