Question

According to equation of continuity when a liquid flows through a tube of variable cross section a with variable velocity v, the quantity that remains constant is

• A. $av^2$
• B. $a^2v$
• C. $\frac{a}{v}$
• D. $av$
• E. $\frac{a^2}{v}$

Answer 1

The Correct Option is D

According to the equation of continuity for a flowing incompressible fluid, the mass flow rate remains constant throughout the tube. The equation is expressed as:

\[ A_1 v_1 = A_2 v_2 \] Where: - \( A \) is the cross-sectional area of the tube, - \( v \) is the velocity of the fluid. This means that the product of the cross-sectional area \( a \) and velocity \( v \) at any point in the tube remains constant. Thus, the quantity that remains constant is: \[ a \cdot v \] Therefore, the correct answer is that the product of the cross-sectional area and velocity remains constant.

Correct Answer:

Correct Answer: (D) \( a \cdot v \)