Question

A pipe which is on a slope, transports water downwards. A doubling of cross sectional area takes place 6 above the reference level. The pressure in the smaller pipe, just before the enlargement, is 860 kPa. The flow velocity in the large pipe is 2,4 m/s. Determine the pressure in kPa at a point 1,5 m above the reference level. Ignore friction losses.

Answer 1

P₂ = 830.75 kPa

Step-by-step explanation:

Given:

Pressure in the smaller pipe,P₁ = 860 kPa

Velocity in the larger pipe, v₂ = 2.4 m/s

Therefore velocity in the smaller pipe, v₁ = 4.8 m/s ( velocity gets doubled since area is reduced to half )

Height at section where the area is doubled, z₁ = 6 m

Height at the section where pressure is to be calculated, z₂ = 1.5 m

Now apply Bernouli Equation between the section of enlargement and at section where pressure is to be calculated,

`(P_(1))/(\rho .g)+(v_(1)^(2))/(2.g)+z_(1) = (P_(2))/(\rho .g)+(v_(2)^(2))/(2.g)+z_(2)`

`(860)/(1000 * 9.81)+(4.8^(2))/(2* 9.81)+6 = (P_(2))/(1000 * 9.81)+(2.4^(2))/(2* 9.81)+1.5`

P₂ = 830.75 kPa

Therefore, pressure at the section 1.5 m above datum is 830.75 kPa