KCET · Physics · Mechanical Properties of Fluids
The cylindrical tube of a spray pump has a cross-section of \(8 \mathrm{~cm}^{2}\), one end of which has 40 fine holes each of area \(10^{-8} \mathrm{~m}^{2}\). If the liquid flows inside the tube with a speed of \(0.15 \mathrm{~m} \mathrm{~min}^{-1}\), the speed with which the liquid is ejected through the holes is
- A \(50 \mathrm{~ms}^{-1}\)
- B \(5 \mathrm{~ms}^{-1}\)
- C \(0.05 \mathrm{~ms}^{-1}\)
- D \(0.5 \mathrm{~ms}^{-1}\)
Answer & Solution
Correct Answer
(B) \(5 \mathrm{~ms}^{-1}\)
Step-by-step Solution
Detailed explanation
According to equation of continuity,
\( a v=\text { constant } \)
\(\therefore \text {For tube, }\left(8 \times 10^{-4}\right) \times\left(\frac{0.15}{60}\right)=a_{1} v_{1} \)
\(\text {For holes, }\left(40 \times 10^{-8}\right) \times v=a_{2} v_{2} \)
\(\therefore a_{2} v_{2}=a_{1} v_{1} \)
\(\therefore 40 \times 10^{-8} \times v=\frac{8 \times 10^{-4} \times 0.15}{60} \)
\(\Rightarrow v=\frac{8 \times 10^{-4} \times 0.15}{40 \times 10^{-8} \times 60} \)
\(=5 \mathrm{~m} / \mathrm{s}\)
\( a v=\text { constant } \)
\(\therefore \text {For tube, }\left(8 \times 10^{-4}\right) \times\left(\frac{0.15}{60}\right)=a_{1} v_{1} \)
\(\text {For holes, }\left(40 \times 10^{-8}\right) \times v=a_{2} v_{2} \)
\(\therefore a_{2} v_{2}=a_{1} v_{1} \)
\(\therefore 40 \times 10^{-8} \times v=\frac{8 \times 10^{-4} \times 0.15}{60} \)
\(\Rightarrow v=\frac{8 \times 10^{-4} \times 0.15}{40 \times 10^{-8} \times 60} \)
\(=5 \mathrm{~m} / \mathrm{s}\)
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