Problem $9$

Water at $70F$ flow by gravity from a large reservoir at a high elevation to a smaller one through a $60-$ft$-$long, $2-$in$-$diameter cast iron piping systems that includes four standard flanged elbows, a wellrounded entrance, a sharp$-$edged exit, and a fully open gate valve. Taking the free surface of the lower reservoir as the reference level, determine the elevation $z_1$ of the higher reservoir for a flow rate of $10f\frac{t^3}{m}in.$

$z_1=12\mathrm{.}6ft$

Problem $10$

A $2\mathrm{.}4-$m$-$diameter tank is initially filled with water $4$ m above the center of a sharp$-$edged $10-$ cm $-$diameter orifice. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere. Neglecting the effect of the kinetic energy correction factor, calculate:

a$)$ The initial velocity from the tank.

b$)$ The time required to empty the tank.

c$)$ The time required to empty the tank if the loss coefficient $K_L$ is not considered.

d$)$ Does the loss coefficient of the orifice cause a significant increase in the draining time of the tank?

$V_2=7\mathrm{.}23\frac{m}{s},t_{K_L}=10\mathrm{.}6$min,$t=8\mathrm{.}7$min,yes, discharge time increases $18\%$

Problem $11$

A $3-$m$-$diameter tank is initially filled with water $2$ m above the center of a sharp$-$edged $10-cm$ diameter orifice. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere through a $100-$m$-$long pipe. The friction coefficient of the pipe is taken to be $0\mathrm{.}015$ and the effect of the kinetic energy correction factor can be neglected. Determine:

a$)$ The initial velocity from the tank.

b$)$ The time required to empty the tank.

c$)$ The time required to empty the tank if pipe length is $L=0.$

$V_2=1\mathrm{.}54\frac{m}{s},t_{100m}=39$min,$t_{0m}=11\mathrm{.}7$min

Problem $12$

Reconsider problem $11.$ In order to drain the tank faster, a pump is installed near the tank exit. Determine how much pump power input is necessary to establish an average water velocity of $4\frac{m}{s}$ when the tank is full at $z=2m.$ Also, assuming the discharge velocity to remain constant, estimate the time required to drain the tank.

$W_{\text{p}\text{u}\text{m}\text{p}}^{}=3\mathrm{.}52kW,t=7\mathrm{.}8$ minutes