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9 Fluid Dynamics
9.2 Problems
9.2.1 Bernoulli’s Equation
9.1 The radius of a water pipe decreases from 10 to 5 cm. If the average velocity in
the wider portion is 4 m/s, find the average velocity in the narrower region.
9.2 Verify if the continuity equation for steady incompressible flow is satisfied for
the following velocity components:
v x = 3x
2
− x y + 2z
2
, v y = 2x
2
− 6x y + y
2
, v z = −2x y − yz + 2y
2
9.3 Air streams horizontally across an aeroplane wing of area 4 m 2 , weighing
300 kg. The air speed is 70 and 55 m/s over the top surface and the bottom
surface, respectively. Find (a) the lift on the wing; (b) the net force on it.
9.4 A venturi meter has a pipe diameter of 20 cm and a throat diameter of 10 cm.
If the water pressure in the pipe is 60,000 Pa and in the throat is 45,000 Pa,
calculate the rate of flow of water in m 3 /s.
9.5 A pitot tube which is used to determine the speed of an aircraft relative to
air is mounted on the wing of a plane. The tube contains alcohol of density
810 kg/m
3 and registers a level difference of 15.0 cm. Assuming that the density of air at NTP is 1.293 kg/m 3 , find the plane’s speed in km/h relative to the
air.
9.6 A garden sprinkler has 80 small holes each 2.5 mm 2 in area. If water is supplied
at the rate of 2 × 10 −3 m 3 /s, find the average velocity of the spray.
9.7 For steady, incompressible flow which of the following values of velocity components are possible?
(a) v x = 3x y + y 2 , v y = 5x y + 2x
(b) v x = 3x 2 + y 2 , v y = −6x y
9.8 If the speed of flow past the lower surface of the wing of an aeroplane is
100 m/s, what speed of flow over the upper surface would give a pressure difference of 1000 Pa? Assume an air density of 1.293 kg/m
3 .
9.9 A venturi meter has a pipe diameter of 4 cm and a throat diameter of 2 cm. The
velocity of water in the pipe section is 10 cm/s. Find (a) the pressure drop; (b)
the velocity in the throat.
9.10 Water is observed to flow through a capillary of diameter 1.0 mm with a speed
of 3 m/s. Viscosity of water in CGS units is
(a) 0.018 at 0 ◦ C
(b) 0.008 at 30 ◦ C
(c) 0.004 at 70 ◦ C
9 Fluid Dynamics
9.2 Problems
9.2.1 Bernoulli’s Equation
9.1 The radius of a water pipe decreases from 10 to 5 cm. If the average velocity in
the wider portion is 4 m/s, find the average velocity in the narrower region.
9.2 Verify if the continuity equation for steady incompressible flow is satisfied for
the following velocity components:
v x = 3x
2
− x y + 2z
2
, v y = 2x
2
− 6x y + y
2
, v z = −2x y − yz + 2y
2
9.3 Air streams horizontally across an aeroplane wing of area 4 m 2 , weighing
300 kg. The air speed is 70 and 55 m/s over the top surface and the bottom
surface, respectively. Find (a) the lift on the wing; (b) the net force on it.
9.4 A venturi meter has a pipe diameter of 20 cm and a throat diameter of 10 cm.
If the water pressure in the pipe is 60,000 Pa and in the throat is 45,000 Pa,
calculate the rate of flow of water in m 3 /s.
9.5 A pitot tube which is used to determine the speed of an aircraft relative to
air is mounted on the wing of a plane. The tube contains alcohol of density
810 kg/m
3 and registers a level difference of 15.0 cm. Assuming that the density of air at NTP is 1.293 kg/m 3 , find the plane’s speed in km/h relative to the
air.
9.6 A garden sprinkler has 80 small holes each 2.5 mm 2 in area. If water is supplied
at the rate of 2 × 10 −3 m 3 /s, find the average velocity of the spray.
9.7 For steady, incompressible flow which of the following values of velocity components are possible?
(a) v x = 3x y + y 2 , v y = 5x y + 2x
(b) v x = 3x 2 + y 2 , v y = −6x y
9.8 If the speed of flow past the lower surface of the wing of an aeroplane is
100 m/s, what speed of flow over the upper surface would give a pressure difference of 1000 Pa? Assume an air density of 1.293 kg/m
3 .
9.9 A venturi meter has a pipe diameter of 4 cm and a throat diameter of 2 cm. The
velocity of water in the pipe section is 10 cm/s. Find (a) the pressure drop; (b)
the velocity in the throat.
9.10 Water is observed to flow through a capillary of diameter 1.0 mm with a speed
of 3 m/s. Viscosity of water in CGS units is
(a) 0.018 at 0 ◦ C
(b) 0.008 at 30 ◦ C
(c) 0.004 at 70 ◦ C