GID $204E$ MOMENTUM TRANSFER

IN$-$CLASS $3$

May $9^{th},2024$

A power$-$law liquid with consistency index $K=0\mathrm{.}223Pa.s^{0\mathrm{.}59},$ flow behavior index $n=0\mathrm{.}59,$ and density $=1200k\frac{g}{m^3}$ is pumped through a pipe having an inside diameter of $0\mathrm{.}0475m$ at a rate of $5\frac{m^3}{h}$ from a tank $A$ to tank $B.$ The level of the liquid in tank $A$ is $2m$ below the pump, while the discharge point is $4m$ above the pump. The suction line is $3m$ long with one $90$ elbow, while discharge line is $6m$ long with two $90$ elbows. Calculate the required pump in $kW.$ The efficiencies of the pump and electric motor are $70\%$ and $80\%,$ respectively. Assume that the level in tank $A$ is constant. Neglect all the sudden enlargements and contractions.

For $90$ elbow and globe valve $\frac{L_e}{D}$ values ad $32$ and $300,$ respectively.

You want to pump a liquid with a viscosity of $5{10}^{-3}Pa.s$ and a density $870k\frac{g}{m^3}$ at a rate of $0\mathrm{.}063\frac{m^3}{s}$ through a piping system which contains $1000ft$ of a $8$ in commercial steel pipe, $4$ globe valves, $16$ gate valves, and $43$ standard $90$ elbows. The discharge end of the piping system is $30ft$ above the entrance and the pressure at both ends is $10g.$ Neglect sudden contractions and enlargements.

a$)$ What pump head is required?

b$)$ If the vapor pressure of the liquid is $5g,$ how far directly above the liquid level in the upstream tank could the pump be located without cavitating?