Question

current attempt in progress
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 increases by a factor of 2.
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 4.
the volume flow rate does not change.

Explanation:

Step1: Recall the formula for volume flow rate

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

Step2: Calculate the new volume flow rate

Let the initial cross - sectional area be \(A_1\) and initial velocity be \(v_1\), so initial volume flow rate \(Q_1=A_1\times v_1\).
The new velocity \(v_2 = 2v_1\) and new cross - sectional area \(A_2=3A_1\).
The new volume flow rate \(Q_2=A_2\times v_2=(3A_1)\times(2v_1)\).
Using the commutative property of multiplication \(Q_2 = 6(A_1\times v_1)\).
Since \(Q_1 = A_1\times v_1\), we have \(Q_2=6Q_1\).

Answer:

The volume flow rate increases by a factor of 6.