Topic IV: Energy Equation and Pipe Flow $(20$ points$)$

Problem $(11)$: Water discharges into the atmosphere from a

tank of depth $(h)$ through a pipe of length $(L),$ and diameter $(d).$

Given the values of $L[m],$ and $d[cm],$ calculate the tank depth

$($h$)$ in $cm$ that could maintain Laminar flow throughout the

pipe with a Reynolds number of $Re=1500.$ Ignore minor losses.

Given

$l=120\mathrm{.}015m$

$d=0\mathrm{.}508m$

Problem $(12)$: A pump is being used to lift water from the bottom

tank to the top tank in a pipe of diameter $(d)$ at a discharge $(Q).$ The

pipe system comprises four regular $90$ flanged elbows. The pipe

entrance is sharp$-$edged, and the pipe exit is sudden. An Angle

Valve $($fully$-$open$)$ is used to control the discharge in the pipeline.

Given the values of $Q[Li\frac{t}{s}],$ and $d[cm],$ calculate the power loss

due to components $($i$.$e$.,$ minor losses$)$ in the pipe $(\{$:$W_{\text{m}\text{i}\text{n}\text{o}\text{r}-\text{l}\text{o}\text{s}\text{s}})$ in

$[$W$].$

Givens:

$Q=8\mathrm{.}8131i\frac{r}{s}$

$d=5\mathrm{.}731cm$

answers:

$453\mathrm{.}648cm$

$782\mathrm{.}03cm$

$720\mathrm{.}176cm41563\mathrm{.}007cm$

$720\mathrm{.}176cm4)563\mathrm{.}007cm$

used to lift water from the botto lar $90$ flanged elbows. The pip hipe exit is sudden. An Ang trol the discharge in the pipeline.

answers:

$295\mathrm{.}09W$

$246\mathrm{.}453W$

$317\mathrm{.}349W$

$340\mathrm{.}867W$

Problem $(13)$: A pump is being used to lift water from the bottom

tank to the top tank in a galvanized iron pipe at a discharge $(Q).$

The length and diameter of the pipe section from the bottom tank

to the pump are $(L_1)$ and $(d_1),$ respectively. The length and

diameter of the pipe section from the pump to the top tank are

$(L_2)$ and $(d_2),$ respectively.

Given the values of $Q[\frac{L}{s}],L_1[m],d_1[m],L_2[m],d_2[m],$

calculate total head loss due to friction $($i$.$e$.,$ major loss$)$ in the

pipe $(\{$:$h_{\text{m}\text{a}\text{j}\text{o}\text{r}-\text{l}\text{o}\text{s}\text{s}})$ in $[$cm$].$

Givens:

$Q=1\mathrm{.}1221i\frac{t}{s},L_2=c5m$ Answers:

$\{$:$[L_1=11502\mathrm{.}646m{d}_2=0\mathrm{.}064m,2)22\mathrm{.}567cm]$

$26\mathrm{.}187cm$

Problem $(14)$: A pump is being used to lift water from an underground

tank through a pipe of diameter $(d)$ at discharge $(Q).$ The total head

loss in the system can be calculated as $(h_L=K[\frac{V^2}{2}g]),$ where $(V)$ is

the flow velocity in the pipe. The elevation difference between the

pump and tank surface is $(h).$

Given the values of $Q[Li\frac{t}{s}],d[cm],$ and $K[-],$ calculate the maximum

elevation difference $h[cm]$ beyond which cavitation would take place

at the pump entrance. Assume turbulent flow conditions.

Givens:

$Q={16\mathrm{.}075}^{1i\frac{t}{5}}$

$d=14\mathrm{.}598cm$

$K=14\mathrm{.}945$

answers:

$940\mathrm{.}645cm$

$58359cm$

$669\mathrm{.}405cm$

$1128\mathrm{.}058cm$