Question

Could you show how to solve this problem (10-25)

1.2. A cast iron pipe with a diameter of 100 mm is used to fill the empty cylindrical tank of diameter 2 m and located at a height of 12 m with water at 25°C. If the power outputf the pump is 4.5 kW, determine the depth of the water in the tank 6 minutes after the pump is turned on. The pipe has a total length of 50 m and frictional (viscous) effects must be considered

Answer 1

neglecting friction loss

considered h = 15 m

water kW =TDH*Q*SG/360

let h=15 m SG=1 as its water

4.5*10³=15 *Q*1/360

Q=108m³/hr

Q=vA

v=108/()=108/ =13750.98m/hr =3.81 m/s

use equation

A cast iron pipe with 100 mm dia ()

assuming water is incompressible

at 25^oC

substituting values in equatoion

f=0.0148

H_L=F*(L/D)*v²/2g

H_L=5.50m

now considering frictional loss

THD = 15+5 =20 m

so

water kW =20*Q*1/360

Q=81 m³/h   

now we have to calculate water depth after 6 min

water added in tank in 6 min = volumetric flowrate *time =81*6/60=8.1m³

now to calculate depth we have to divide volume by area of tank =8.1/ =2.5783 m