KCET · Physics · Mechanical Properties of Fluids
An ideal fluid flows through a pipe of circular cross section with diameters \( 5 \mathrm{~cm} \) and \( 10 \mathrm{~cm} \) as shown. The ratio of velocities of fluid at \( A \) and \( B \) is
- A 1:1
- B \( 1: 4 \)
- C 2:1
- D \( 1: 2 \)
Answer & Solution
Correct Answer
(A) 1:1
Step-by-step Solution
Detailed explanation
An ideal fluid flow through the pipe as shown in the following figure.
Now, (Area) \( _{A} v_{A}=(\text { Area })_{B} v_{B} \)
\(\Rightarrow \frac{v_{A}}{v_{B}}=\frac{(\text { area })_{B}}{(\text { area })_{A}}=\frac{\Pi \times 10^{2}}{\Pi \times 5^{2}}=\frac{100}{25}=\frac{4}{1}\)
Therefore, ratio of velocities of fluid at \( A \) and \( B \) is \( 4: 1 \).
Now, (Area) \( _{A} v_{A}=(\text { Area })_{B} v_{B} \)
\(\Rightarrow \frac{v_{A}}{v_{B}}=\frac{(\text { area })_{B}}{(\text { area })_{A}}=\frac{\Pi \times 10^{2}}{\Pi \times 5^{2}}=\frac{100}{25}=\frac{4}{1}\)
Therefore, ratio of velocities of fluid at \( A \) and \( B \) is \( 4: 1 \).
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