Daniel B. answered • 12/10/23
A retired computer professional to teach math, physics
I assume this is a steady state situation.
That is, water is continuously flowing through all sections of the pipe.
This is in contrast to a situation where water start flowing through the
first segment before it hits the second segment.
Under the assumption of steady flow,
each second, the same volume of water passes through each segment.
The second segment has double the diameter of the first,
therefore the cross section of the second segment is four times larger than
the cross section of the first segment.
Therefore water needs to flow through the second segment four time slower
so as to pass the same volume.
That is, the speed in the second segment is 1.0 m/s.
The third segment has diameter half the first, therefore its cross section is four times smaller.
Therefore the water must flow four times faster, i.e., 16 m/s.
To answer question 2. we can use any of the three segments.
Let me use the second segment.
Its cross section is 4π(2.0 cm/2)² = 4π cm²
The volume flow rate is calculated as the cross section times speed,
which gives 4π cm² ×1.0 m/s = 4π cm² × 100 cm/s = 400π cm³/s
