Answer the following a write down on a paper and photos or image will be appreciated? Question FOUR

a$)$ Two tanks with external orifices in the same vertical plane are as shown in figure

$3\mathrm{.}0.$Determine the spacing $\text{'}x\text{'}$ for the jets to intersect at the plane of the bases.

$Cd=0-8555$

$(10$Marks$)$Question TWO

From the basic assumptions, derive the equation for determining the loss through a pipe of

length $L.,$ when the flow is steady, uniform and incompressible.

$(20$Marks$)$

Question THREE

$($a$)$ A divergent convergent mouth piece is fitted on the vertical side of a tank as shown in $2\mathrm{.}0.$

The head over the centre of the mouth piece is $2\mathrm{.}0$ m $.$ If the mouth piece discharges $360$

lpm of water into the atmosphere, determine the throat and exit diameters, assuming that:

i$)$ pressure in the throat should not fall more than $7\mathrm{.}5$ m below atmospheric

ii$)$ No loss in the convergent portion and the loss in the divergent portion is one$-$fifth

of the velocity head at exit.

$($b$)$ A jet of water is initially $100$ mm in diameter and, when directed vertically upwards,

reaches a maximum height of $20$ m $.$ Assuming that the jet remains circular, determine the

dixharge and the diameter of the jet at $10$ m height. Question ONE

Figure $1\mathrm{.}0$ shows a two looped pipe network and the hydraulic particulars as indicated. Estimate the flows in the various pipes for one approximation, using the Hardy$-$cross method. The pipe diameters are $500$ mm throughout.

Take $f=0\mathrm{.}005$ for each pipe.

$(30$Marks$)$

Fig. $1\mathrm{.}0$

Fig. $3\mathrm{.}0$

$($b$)$ In a pipeline carrying water, section B is $2$ m higher than section A $.$ The diameters and the

pressures at A and $B$ are as shown in table $1\mathrm{.}0.$ If the velocity at section $A$ is $1\frac{m}{s},$

determine the direction of flow. Neglect all the losses

$(10$Marks$)$

Table $1\mathrm{.}0$

Question FIVE

$($a$)$ A pipe carries water such that the local velocities at the centre of the pipe $y=R$ and at $y=\frac{R}{2}$

were $1\mathrm{.}5\frac{m}{s}$ and $1\mathrm{.}36\frac{m}{s}$ respectively. If the diameter of the pipe is $25$ cm $,$ determine the discharge,

friction factor, and the roughness projection from the pipe wall.

$($b$)$ Using the Hazen $-$ William's approach, derive a $Q^n-$ law for computing friction head loss

in a pipeline system.

v$)$ Density

vi$)$ Specific gravity

c$)$ Calculate the following for a liquid volume $1\mathrm{.}0$ lit. and specific gravity $0\mathrm{.}7$

i$)$ Density

ii$)$ Specific weight

iii$)$ Weight

Question TWO

a$)$ A mercury U$-$tube manometer set$-$up to measure the pressure above atmospheric of

water in a pipeline, the water being in contact with the mercury in the left limb if the

mercury is $300$ mm below $A$ as in $($figure $1)$ in the left hand limb and $200$ mm above $A$

in right hand limb$,$ determine the gauge pressure at A take specific gravity of mercury

$=13\mathrm{.}6(8$marks$)$

b$)$ A U$-$tube manometer $($figure $2)$ measures the pressure between two points A and B in a

pipeline. The liquids in the pipeline and manometer have a specific weight as shown in sketch

Determine the pressure difference between points A and B

Given that the liquid in both pipe A and B is water while the manometric fluid is mercury and

that $a=1500mm,b=750mm$ and $h=500mm$ and the liquid at A and B is water

$(W_1=9\mathrm{.}81{10}^3\frac{N}{m^3})$ and the specific gravity of mercury is $13\mathrm{.}6($so that $W_2=13\mathrm{.}6W_1)$

$(12$marks$)$