Question:
A liquid is allowed to flow into a tube of truncated cone shape. Identify the correct statement:
A liquid is allowed to flow into a tube of truncated cone shape. Identify the correct statement:
Show Hint
The principle of continuity implies that for an incompressible fluid, as the cross-sectional area decreases, the velocity must increase to maintain constant mass flow.
Updated On: Mar 28, 2026
- The speed is high at the wider end and high at the narrow end.
- The speed is low at the wider end and high at the narrow end.
- The speed is same at both ends in a streamline flow.
- The liquid flows with uniform velocity in the tube.
Show Solution
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The Correct Option is B
Solution and Explanation
According to the principle of continuity for an incompressible fluid:
\[
A_1v_1 = A_2v_2,
\]
where \( A \) is the cross-sectional area and \( v \) is the velocity of the fluid.
In a truncated cone, the cross-sectional area at the wider end (\( A_1 \)) is greater than the area at the narrower end (\( A_2 \)). Hence, the velocity at the wider end (\( v_1 \)) is smaller, and the velocity at the narrower end (\( v_2 \)) is higher to conserve mass flow:
\[
v_1<v_2.
\]
Final Answer:
\[
\boxed{\text{The speed is low at the wider end and high at the narrow end.}}
\]
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