Mechanics of Fluids

main. The depth of water in the tank is to be increased from
0.1 m to 2.7 m in not more than 15 minutes. Assuming that f
has the constant value 0.007, and neglecting energy losses other
than pipe friction, determine the diameter of pipe required.
7.26 A viscometer consists essentially of two reservoirs joined by a
length of capillary tubing. The instrument is filled with liquid
so that the free surfaces in the reservoirs are where the walls
are in the form of vertical circular cylinders, each of diameter
20 mm. The capillary tube is 1 mm diameter and 400 mm long.
Initially the difference in the free surface levels is 40 mm, and,
for a particular liquid of relative density 0.84, the time taken
for the higher level to fall by 15 mm is 478 s. Neglecting end
effects in the capillary tube and energy losses other than those
due directly to viscosity, determine the viscosity of the liquid.
7.27 Water flows at a steady mean velocity of 1.5 m · s −1 through a
50 mm diameter pipe sloping upwards at 45 ◦ to the horizontal.
At a section some distance downstream of the inlet the pressure
is 700 kPa and at a section 30 m further along the pipe the
pressure is 462 kPa. Determine the average shear stress at the
wall of the pipe and at a radius of 10 mm.
7.28 A fluid of constant density ϱ enters a horizontal pipe of radius
R with uniform velocity V and pressure p1. At a downstream
section the pressure is p2 and the velocity varies with radius
r according to the equation u = 2V{1 − (r 2 /R 2 )}. Show that
the friction force at the pipe walls from the inlet to the section
considered is given by πR 2 (p1 − p2 − ϱV 2 /3).
Problems 297