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

Answer:

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

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

⇒ $A_{1}$ × $V_{1}$ = $A_{2}$ × $V_{2}$

⇒  $\frac{\pi }{4}$ × $d_{1} ^{2}$ × $V_{1}$ =

⇒  $d_{1} ^{2}$ × $V_{1}$ =  $d_{2} ^{2}$  × $V_{2}$

⇒  $(3.2)^{2}$ × 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