Mechanics of Fluids

How are the running costs altered if n pipes of equal diameter
are used in parallel to give the same total flow rate at the same
Reynolds number as for a single pipe?
7.15 A pump delivers water through two pipes laid in parallel. One
pipe is 100 mm diameter and 45 m long and discharges to atmosphere
at a level 6 m above the pump outlet. The other pipe,
150 mm diameter and 60 m long, discharges to atmosphere at
a level 8 m above the pump outlet. The two pipes are connected
to a junction immediately adjacent to the pump and both
have f = 0.008. The inlet to the pump is 600 mm below the
level of the outlet. Taking the datum level as that of the pump
inlet, determine the total head at the pump outlet if the flow rate
through it is 0.037 m 3 · s −1 . Losses at the pipe junction may be
neglected.
7.16 A reservoir A, the free water surface of which is at an elevation
of 275 m, supplies water to reservoirs B and C with water
surfaces at 180 m and 150 m elevation respectively. From A to
junction D there is a common pipe 300 mm diameter and 16 km
long. The pipe from D to B is 200 mm diameter and 9.5 km
long while that from D to C is 150 mm diameter and 8 km long.
The ends of all pipes are submerged. Calculate the rates of flow
to B and C, neglecting losses other than pipe friction and taking
f = 0.01 for all pipes.
7.17 A reservoir A feeds two lower reservoirs B and C through a
single pipe 10 km long, 750 mm diameter, having a downward
slope of 2.2 × 10 −3 . This pipe then divides into two branch
pipes, one 5.5 km long laid with a downward slope of 2.75 ×
10 −3 (going to B), the other 3 km long having a downward slope
of 3.2 × 10 −3 (going to C). Calculate the necessary diameters
of the branch pipes so that the steady flow rate in each shall be
0.24 m 3 · s −1 when the level in each reservoir is 3 m above the
end of the corresponding pipe. Neglect all losses except pipe
friction and take f = 0.006 throughout.
7.18 A pipe 600 mm diameter and 1 km long with f = 0.008
connects two reservoirs having a difference in water surface
level of 30 m. Calculate the rate of flow between the reservoirs
and the shear stress at the wall of the pipe. If the upstream half
of the pipe is tapped by several side pipes so that one-third of
the quantity of water now entering the main pipe is withdrawn
uniformly over this length, calculate the new rate of discharge
to the lower reservoir. Neglect all losses other than those due
to pipe friction.
7.19 A rectangular swimming bath 18 m long and 9 m wide has a
depth uniformly increasing from 1matoneendto2matthe
other. Calculate the time required to empty the bath through
two 150 mm diameter outlets for which C d = 0.9, assuming
that all condition hold to the last.
Problems 295