Fluid Mechanics – 2
Problem: As shown in the figure, an incompressible liquid can be steadily siphoned from a
container provided that: the inlet of the tube is very close to the free surface in the container,
point (1); the end of the tube, point (3), is below the point (1); and the maximum elevation of the
tube, point (2), is “not too great.” Consider water at 20°C being siphoned from a very large tank
(i.e., significantly larger than the hose diameter) through a hose of constant diameter d = 3 cm as
shown. The end of the siphon is 1.5 m below the bottom of the tank, and the atmospheric
pressure is 1.013 x 105 Pa. Note: At 20°C, vapor pressure of water is ~1765 Pa, specific weight
of water γwater = 9.8 x 103 N/m3, and acceleration of gravity g = 9.8 m/s2, and the length of the
hose is 12 m.
Questions:
a) (25 points) Assuming it is inviscid fluid, determine the fluid speed in the hose.
b) (25 points) For this inviscid fluid, determine the maximum height of the hill, H, over
which the water can be siphoned without cavitation occurring (no vapor generated inside
the tube).
c) (40 points) If the fluid is viscous and Darcy friction factor f = 0.02 in the hose, calculate
the velocity of fluid inside the hose. If H is maintained at the same level as in question b)
and the length of the pipe from the inlet to point (2) is 6 m, will cavitation occur or not?
Explain your answer.
d) (10 points) Given dynamic viscosity of water µ= 1.0 x 10-3 kg/m·s, is the flow in question
c) laminar or turbulent? Explain your answer.
Fall 2016