Question

current attempt in progress

in the drawing, water flows from a wide section of a pipe to a narrow section. in which part of the pipe is the volume flow rate the greatest?

the narrow section.
the wide section.
the volume flow rate is the same in both sections of the pipe.

Explanation:

Step1: Recall the equation of continuity

The equation of continuity for an incompressible fluid is \(A_1v_1 = A_2v_2\), where \(A\) is the cross - sectional area of the pipe and \(v\) is the speed of the fluid. The volume flow rate \(Q\) is given by \(Q=Av\).

Step2: Analyze the volume flow rate

Since water is an incompressible fluid (density \(
ho\) is constant) and there is no source or sink of water in the pipe (steady - state flow), from the equation of continuity \(Q_1 = Q_2\). The volume flow rate \(Q\) (where \(Q = Av\)) must be the same throughout the pipe. The speed \(v\) changes (increases in the narrow section as \(A\) decreases, since \(v=\frac{Q}{A}\)), but the volume flow rate \(Q\) remains constant.

Answer:

The volume flow rate is the same in both sections of the pipe.