Question

Water is traveling through a horizontal pipe with a speed of 1.7 m/s and at a pressure of 205 kPa. This pipe is reduced to a new pipe which has a diameter half that of the first section of pipe. Determine the speed and pressure of the water in the new, reduced in size pipe.

Answer 1

The velocity is
`v_2 = 6.8 \ m/s`

The pressure is
`P_2 = 204978 Pa`

Step-by-step explanation:

From the question we are told that

The speed at which water is travelling through is
`v = 1.7 \ m/s`

The pressure is
`P_1 = 205 k Pa = 205 *10^(3) \ Pa`

The diameter of the new pipe is
`d = (D)/(2)`

Where D is the diameter of first pipe

According to the principal of continuity we have that

`A_1 v_1 = A_2 v_2`

Now
`A_1` is the area of the first pipe which is mathematically represented as

`A_1 = \pi (D^2)/(4)`

and
`A_2` is the area of the second pipe which is mathematically represented as

`A_2 = \pi (d^2)/(4)`

Recall
`d = (D)/(2)`

`A_2 = \pi ([ D^2])/(4 *4)`

`A_2 = (A_1)/(4)`

So
`A_1 v_1 = (A_1)/(4) v_2`

substituting value

`1.7 = (1)/(4) * v_2`

`v_2 = 4 * 1.7`

`v_2 = 6.8 \ m/s`

According to Bernoulli's equation we have that

`P_1 + \rho (v_1 ^2)/(2) = P_2 + \rho (v_2 ^2)/(2)`

substituting values

`205 *10^(3 )+ (1.7 ^2)/(2) = P_2 + (6.8 ^2)/(2)`

`P_2 = 204978 Pa`