Question

Water flows through a hosepipe whose internal diameter is 2 cm at a speed of 1 m by second.what should be the diameter of the hole if the water is to emerged at speed of 4 m/s?

Answer 1

1 cm

Explanation:

We know that the amount of water that flows is a constant.

Therefore, the volume per time is conserved.

That means the area times the flow rate is conserved, or
`A_1 r_1 = A_2 r_2`

We can write the area of a round tube:
`pi/4 d_1^2r_1 = pi/4 d_2^2r_2`
i.e. the second diameter has to be
`d_1^2r_1 = d_2^2r_2 implies d_2 = d_1 cdot sqrt((r_1)/(r_2))`

hence,
`d_2 = 2\ cm cdot sqrt((1\ m/s) / (4\ m/s)) = 1\ cm`