Mechanics of Fluids

∴ Velocity of approach = 0.0660 m3 · s−1 0.26 m2 = 0.254 m · s −1
u2 1
2g = (0.254 m · s−1 ) 2
19.62 m · s−2 = 3.28 × 10−3 m
∴ H + u 2 1 /2g = (0.155 + 0.00328) m = 0.1583 m
Second approximation: Q = 2
3 0.61� (19.62)0.6(0.1583) 3/2 m 3 · s −1
= 0.0681 m 3 · s −1
Further refinement of the value could be obtained by a new calculation
of u1(0.0681 m 3 · s −1 ÷0.26 m 2 ), a new calculation of H +u 2 1 /2g
and so on. One correction is usually sufficient, however, to give a value
of Q acceptable to three significant figures. ✷
PROBLEMS
3.1 A pipe carrying water tapers from a cross-section of 0.3 m 2 at
A to 0.15 m 2 at B which is 6 m above the level of A. AtA
the velocity, assumed uniform, is 1.8 m · s −1 and the pressure
117 kPa gauge. If frictional effects are negligible, determine the
pressure at B.
3.2 A long bridge with piers 1.5 m wide, spaced 8 m between
centres, crosses a river. The depth of water before the bridge is
1.6 m and that between the piers is 1.45 m. Calculate the volume
rate of flow under one arch assuming that the bed of the river is
horizontal, that its banks are parallel and that frictional effects
are negligible.
3.3 A pipe takes water from a reservoir where the temperature is
12 ◦ C to a hydro-electric plant 600 m below. At the 1.2 m
diameter inlet to the power house the gauge pressure of the
water is 5.5 MPa and its mean velocity 2 m · s −1 . If its temperature
there is 13.8 ◦ C at what rate has heat passed into
the pipe as a result of hot sunshine? (Note: The change of
atmospheric pressure over 600 m must be accounted for: mean
atmospheric density = 1.225 kg · m −3 . Specific heat capacity of
water = 4.187 kJ · kg −1 · K −1 .)
3.4 In an open rectangular channel the velocity, although uniform
across the width, varies linearly with depth, the value at the free
surface being twice that at the base. Show that the value of the
kinetic energy correction factor is 10/9.
3.5 From a point 20 m away from a vertical wall a fireman directs
a jet of water through a window in the wall at a height of
15 m above the level of the nozzle. Neglecting air resistance
Problems 131