Question

A rectangular shower head has 25
circular openings of radius 1 mm each.
The pipe connecting the shower head has
a radius 6 mm. If the water flows in the
pipe at the rate of 5m/s, then calculate
the speed of water leaving the openings
of the shower head.​

Answer 1

Given:

A rectangular shower head has 25  circular openings of radius 1 mm each.The pipe connecting the shower head has a radius 6 mm. If the water flows in the  pipe at the rate of 5 m/s.

To Find:

What is the speed of water leaving the openings  of the shower head?​

Solution:

Radius of circular shower head = r = 1 mm = 0.001 m

Number of circular shower head = N = 25

Radius of pipe = R = 6 mm = 0.006 m

Speed of water in pipe $\mathbf{=u = 5 \ \frac{m}{s}}$

Speed of water from circular shower head = v = Unknown

We know formula of mass of continuity equation:

Total flow rate from circular shower head = total flow rate in pipe

$\mathbf{N\times \pi \times r^{2}\times v=\pi \times R^{2}\times u}$

$\mathbf{25\times \pi \times 0.001^{2}\times v=\pi \times 0.006^{2}\times 5}$

On simplify:

$\mathbf{v= 7.2 \ \ \frac{m}{s}}$

Means speed of water leaving the opening of shower head is 7.2 m/s.