The flow velocity in a 2.5-cm-diameter tube is 0.015 m/s. If a tube restriction narrows the tube down to 1.5 cm in diameter, the flow in this region is
A) 0.009 m/s.
B) 0.025 m/s.
C) 0.042 m/s
D) 0.051 m/s.

Question

Quizplus · Accepted Answer

The flow rate in a tube is constant, so we use the equation of continuity: $A_1v_1 = A_2v_2$, where $A_1$ and $A_2$ are the cross-sectional areas of the tube before and after the restriction, and $v_1$ and $v_2$ are the velocities of the fluid before and after the restriction, respectively. The area of a circle is given by $A = \pi r^2$, so we can substitute the diameters given (divided by 2 to get the radius) into the equation: $\pi(1.25^2)0.015 = \pi(0.75^2)v_2$. Solving for $v_2$ gives approximately 0.042 m/s.

The Flow Velocity in a 2