Question

a hollow pipe is submerged in a stream of water so that the length of the pipe is parallel to the velocity of the water. if the water speed doubles and the cross - sectional area of the pipe triples, what happens to the volume flow rate of the water passing through it?
the volume flow rate does not change.
the volume flow rate increases by a factor of 3.
the volume flow rate increases by a factor of 6.
the volume flow rate increases by a factor of 2.
the volume flow rate increases by a factor of 4.

Explanation:

Step1: Recall the formula for volume flow rate

The volume flow rate \(Q\) is given by \(Q = A\times v\), where \(A\) is the cross - sectional area and \(v\) is the velocity.

Step2: Analyze the changes

Let the initial area be \(A_1\) and initial velocity be \(v_1\), so initial flow rate \(Q_1=A_1v_1\).
The new area \(A_2 = 3A_1\) and new velocity \(v_2=2v_1\).
The new flow rate \(Q_2=A_2v_2=(3A_1)\times(2v_1)\).

Step3: Calculate the ratio of new to old flow rate

\(\frac{Q_2}{Q_1}=\frac{3A_1\times2v_1}{A_1v_1}=6\)

Answer:

The volume flow rate increases by a factor of 6.