Question

A pipe leads from a storage tank on the roof of a building to the ground floor. The absolute pressure of the water in the storage tank where it connects to the pipe is 3.0×105Pa, the pipe has a radius of 1.0 cm where it connects to the storage tank, and the speed of flow in this pipe is 1.6 m/s. The pipe on the ground floor has a radius of 0.50 cm and is 9.0 m below the storage tank. Find the speed of flow in the pipe on the ground floor.

Answer 1

6.4 m/s

Step-by-step explanation:

From the equation of continuity

A1V1=A2V2 where A1 and V1 are area and velocity of inlet respectively while A2 and V2 are the area and velocity of outlet respectively

`A1=\pi (r1)^(2)`

`A2=\pi (r2)^(2)`

where r1 and r2 are radius of inlet and outlet respectively

v1 is given as 1.6 m/s

Therefore

`\pi (0.01)^(2)* 1.6 = \pi (0.005)^(2)v2`

`V2=\frac {\pi (0.01)^(2)* 1.6}{\pi (0.005)^(2)}=6.4 m/s`