Question

The head-discharge relationship for a certain pump can be represented by the equation H = 28-9Q2. The pump is fixed 2.5 m above the water surface in a river and it forces the water to a level 7.8 m above the pump. The suction and delivery pipes are 16 m and 764 m long, respectively and each pipe is 0.8 m in diameter. The pipe coefficient of friction is 0.005. The friction coefficient (Km) for the pump is 1.5. Estimate the time required to lift 1500 tons of water from the river by using this pump.

Answer 1

The time required to lift 1500 tons was estimated.

Step-by-step explanation:

Given data,

Head discharge H = 28-9
`Q^(2)`

`z_(1)` = 2.5 m

`z_(2)` = 7.8 m

The suction pipe
`L_(1)` = 16 m

The delivery pipe
`L_(2)` = 764 m

Diameter d = 0.8 m

coefficient of friction f = 0.005

coefficient of friction (km) pump = 1.5

H = 28-9
`Q^(2)`

The total head H =
`z_(1)` +
`z_(2)` + h
`L_(1)` + h
`L_(2)`

h
`L_(1)` =
`(fL_(1)v^(2) )/(2gd)`

h
`L_(2)` =
`(fL_(2)v^(2) )/(2gd)`

H =
`z_(1)` +
`z_(2)` +
`(fL_(1)v^(2) )/(2gd)` +
`(fL_(2)v^(2) )/(2gd)`

H = 2.5 + 7.8 +
`((0.005)(16)(v^(2)) )/((2)(9.8)(0.8))` +
`((0.005)(764)(v^(2)) )/((2)(9.81)(0.8))`

H = 10.3+0.051
`v^(2)` + 2.43
`v^(2)`

H = 10.3 + 2.48
`v^(2)`

28-9
`Q^(2)` = 10.3 + 2.48
`v^(2)`

V =
`(Q)/(A)` =
`(Q)/((2.0)/(4) )` = 2Q