$20/05/2024$

Chemical engineering equipment: Deadline: $\frac{03}{06}\frac{?}{2024}$

Problem $8$

Water needs to be pumped through a horizontal steel pipe with a diameter of $5cm$ and a length of $40$ meters at a desired flow rate of $0\mathrm{.}08\frac{m^3}{s}.$

a$)$ Assuming a smooth steel pipe, estimate the pressure drop due to friction in the pipe using the Darcy$-$Weisbach equation. Find the friction factor $($f$)$ for smooth steel pipes at the specific Reynolds number for this flow.

b$)$ Considering only pressure drop, determine the minimum pump head required in meters of water to overcome the pressure loss and maintain the desired flow rate.

c$)$ Given the water density $()$ is $1000k\frac{g}{m^3},$ calculate the pressure drop $(P)$ in Pascals $(Pa).$

d$)$ Assuming a pump efficiency of $90\%,$ calculate the shaft power $(P)$ required by the pump in Watts $($W$)$ to deliver the desired flow rate. $($Hint: Pump efficiency relates the ideal power to the actual shaft power needed$).$

Data:

Pipe diameter $(D)=0\mathrm{.}05m$

Pipe length $(L)=40m$

Flow rate $(Q)=0\mathrm{.}08\frac{m^3}{s}$

Water density $()=1000k\frac{g}{m^3}$

Pump efficiency $()=90\%($assumed$)$