Question

A liquid is allowed to flow into a tube of truncated cone shape. Identify the correct statement:

• A. The speed is high at the wider end and high at the narrow end.
• B. The speed is low at the wider end and high at the narrow end.
• C. The speed is same at both ends in a streamline flow.
• D. The liquid flows with uniform velocity in the tube.

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.

Answer 1

The Correct Option is B

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: \[ \boxed{\text{The speed is low at the wider end and high at the narrow end.}} \]