Question

1. Water flows from a hose-pipe of internal diameter 1 cm at a rate
of 5 litres per minute. At what speed is the water flowing through
the pipe?​

Answer 1

1 litre = 1000 cubic centimeters

In the question, 5000 ccs pass every minute.

Think of that as a rod of of water, 1cm in diameter

Volume = length*area = 5000 cc

length = volume/area

area = pi*r^2, where r = radius of pipe.

r = 0.5 cm (half the diameter)

length = 5000/(pi*(0.5)^2) cm

= 20000/pi cm

That's the length per minute, so the speed is

(20000/pi) cm/minute<<<

(20000/(60*pi)) cm/second<<<

hope it will help you!!❤️

Answer 2

The speed of water flowing through the pipe = (10/$\pi$) meter/second

Explanation:

Given,

         Rate of water flow from the pipe = 5 litres/minute i.e., 5000 $cm^{3}$

                                                                                                   (1 litre = 1000 $cm^{3}$)

         So from the above, the volume (V) of the pipe = 5000 $cm^{3}$

         Also given,

                          the diameter of the pipe = 1 cm

        So,

                          the radius of the pipe (r) = 1/2 cm

Let us imagine a pipe through which water is flowing...

According to formula,

           Volume (V) of the pipe = $\pi$ * $r^{2}$ * h                      ,h is the height of pipe

So here, the volume of the pipe (V) = $\pi$ * $(1/2)^{2}$ * h

h = 5000 / $\pi$ * $(1/2)^{2}$

= 20000/$\pi$ cm           i.e., the length of the pipe

As we know,

         Speed = length * time

hence,

        The speed of the pipe per minute = 20000/$\pi$ * 60      (1 min = 60 sec)

                                                                  = 1000/$\pi$  cm/second  

                                                                                                (1 meter = 100 cm)

                                                                  = 10/$\pi$  meter/second