Problem $5$

Engine oil at $40C$ is flowing through a $1\mathrm{.}5-cm-$diameter pipe that discharges into the atmosphere at $88$ kPa $.$ The absolute pressure $15$ m before the exit is measured to be $135$ kPa $.$ Determine the flow rate of oil through the pipe if the pipe is:

a$)$ Horizontal.

b$)$ Inclined $8$ upward from the horizontal.

c$)$ Inclined $8$ downward from the horizontal.

$V_{\text{h}\text{o}\text{r}\text{i}\text{z}}^{}=1\mathrm{.}79{10}^{-5}\frac{m^3}{s},V_{+8}^{}=1\mathrm{.}1{10}^{-5}\frac{m^3}{s},V_{-8}^{}=2\mathrm{.}47{10}^{-5}\frac{m^3}{s}$

Problem $6$

Glycerin at $40C$ is flowing through a $2-cm-$diameter, $25-$m$-$long pipe that discharges into the atmosphere at $100$ kPa $.$ The flow rate through the pipe is $0\mathrm{.}048\frac{L}{s}.$ Determine:

a$)$ If the flow is laminar or turbulent.

b$)$ The absolute pressure $25$ m before the pipe exit.

c$)$ At what angle $$ must the pipe be inclined downward from the horizontal for the pressure in the entire pipe to be atmospheric pressure and the flow rate to be maintained the same?

$P_1=194$kPa,$=-17\mathrm{.}6$

Problem $7$

Consider flow from a water reservoir through a circular hole of diameter D at the side wall at a vertical distance H from the free surface. The flow rate through an actual hole with a sharp$-$edged entrance $(K_L=0\mathrm{.}5)$ is considerably less that the flow rate calculated assuming "frictionless" flow and thus zero loss for the hole. Disregarding the effect of the kinetic energy correction factor, obtain a relation for the "equivalent diameter" of the sharp$-$edged hole for use in frictionless flow relations.

$D_{\text{e}\text{q}\text{u}\text{i}\text{v}}=0\mathrm{.}904D$

Problem $8$

A horizontal pipe has an abrupt expansion from $8$ cm to $16$ cm $.$ The water velocity in the smaller section is $10\frac{m}{s}$ and the flow is turbulent. The pressure in the smaller section is $P_1=410$kPa. Taking the kinetic energy correction factor to be $1\mathrm{.}06$ at both the inlet and the outlet, determine the downstream pressure $P_2$ and estimate the error that would have occurred if Bernoulli's equation had been used.

$P_2=432$kPa,$=6\%$