Question

To water the yard you use a hose with a diameter of 3.2 cm. Water flows from the hose with a speed of 1.1 m/s. If you partially block the hose so that the effective diameter is now 0.57 cm, with what speed does the water now flow from the hose

Answer 1

The speed of water flow inside the pipe at point - 2 = 34.67 m / sec

Step-by-step explanation:

Given data

Diameter at point - 1 = 3.2 cm

Velocity at point - 1 = 1.1 m / sec = 110 cm / sec

Diameter at point - 2 = 0.57 cm

Velocity at point - 2 = ??

We know that from the continuity equation the rate of flow is constant inside a pipe between two points.

Thus

⇒
`A_(1)` ×
`V_(1)` =
`A_(2)` ×
`V_(2)`

⇒
`(\pi )/(4)` ×
`d_(1) ^(2)` ×
`V_(1)` =

⇒
`d_(1) ^(2)` ×
`V_(1)` =
`d_(2) ^(2)` ×
`V_(2)`

⇒
`(3.2)^(2)` × 110 =
`(0.57)^(2)` ×
`V_(2)`

⇒
`V_(2)` = 3467 cm / sec

⇒
`V_(2)` = 34.67 m / sec

Thus the speed of water flow inside the pipe at point - 2 = 34.67 m / sec