Mechanics of Fluids

132 The principles governing fluids in motion
determine the angle at which the nozzle must be held when the
supply pressure at the nozzle is only just sufficient, and calculate
this minimum pressure if Cv for the nozzle is 0.95. (The velocity
head in the hose may be neglected.)
3.6 The air supply to an oil-engine is measured by being taken
directly from the atmosphere into a large reservoir through a
sharp-edged orifice 50 mm diameter. The pressure difference
across the orifice is measured by an alcohol manometer set at
a slope of arcsin 0.1 to the horizontal. Calculate the volume
flow rate of air if the manometer reading is 271 mm, the relative
density of alcohol is 0.80, the coefficient of discharge for
the orifice is 0.602 and atmospheric pressure and temperature
are respectively 755 mm Hg and 15.8 ◦ C. (You may assume
R = 287 J · kg −1 · K −1 .)
3.7 Oil of relative density 0.85 issues from a 50 mm diameter orifice
under a pressure of 100 kPa (gauge). The diameter of the vena
contracta is 39.5 mm and the discharge is 18 L · s −1 . What is
the coefficient of velocity?
3.8 A submarine, submerged in sea-water, travels at 16 km · h −1 .
Calculate the pressure at the front stagnation point situated
15 m below the surface. (Density of sea-water =
1026 kg · m −3 .)
3.9 A vertical venturi-meter carries a liquid of relative density 0.8
and has inlet and throat diameters of 150 mm and 75 mm
respectively. The pressure connection at the throat is 150 mm
above that at the inlet. If the actual rate of flow is 40 L · s −1
and the coefficient of discharge is 0.96, calculate (a) the pressure
difference between inlet and throat, and (b) the difference
of levels in a vertical U-tube mercury manometer connected
between these points, the tubes above the mercury being full of
the liquid. (Relative density of mercury = 13.56.)
3.10 A servo-mechanism is to make use of a venturi contraction in
a horizontal 350 mm diameter pipe carrying a liquid of relative
density 0.95. The upper end of a vertical cylinder 100 mm
diameter is connected by a pipe to the throat of the venturi
and the lower end of the cylinder is connected to the inlet.
A piston in the cylinder is to be lifted when the flow rate
through the venturi exceeds 0.15 m 3 · s −1 . The piston rod is
20 mm diameter and passes through both ends of the cylinder.
Neglecting friction, calculate the required diameter of
the venturi throat if the gross effective load on the piston rod
is 180 N.
3.11 A sharp-edged notch is in the form of a symmetrical trapezium.
The horizontal base is 100 mm wide, the top is 500 mm wide
and the depth is 300 mm. Develop a formula relating the discharge
to the upstream water level, and estimate the discharge
when the upstream water surface is 228 mm above the level