Chapter I
1. Bernoulli’s equation states that the energy per unit mass of a steady incompressible flow of an
inviscid fluid is constant. Show that the units in SI and English systems are the same for each
term of the equation.
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2. What is the kinematic viscosity (ν) of water in units of m2/s for a dynamic viscosity (µ) of
1.20×10-3 N s/m2 and a density of 999 kg/m3?
3. The velocity profile for a laminar flow in a round pipe is given by the equation
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where umax is the centerline velocity, R is the pipe radius, and r is the radial distance from the
pipe centerline.
i) What is the velocity gradient at the pipe wall? Note that the normal distance from the pipe
wall is y=R-r; thus, dy = – dr, and du/dy = -du/dr.
ii) What is the shear stress at the pipe centerline?
iii) Show that the velocity gradient, and hence the shear stress varies linearly from zero at the
pipe centerline to a maximum at the pipe wall.
4. A rod 150 mm in diameter moves along its axis at 0.15 m/s inside a concentric cylinder 150.4
mm in diameter and 1.10 m long. The space between them is filled with an oil of specific gravity
0.82 and kinematic viscosity ν = 10-4 m2/s. a) what is the viscous force resisting the motion? b) If
the viscous force were twice of that calculated in a) what would the rod speed be?
Rod
V = 0.15 m/s
5. The viscosity of a fluid is to be measured by a viscometer constructed of two 75–cm–long
concentric cylinders. The outer diameter of the inner cylinder is 15 cm, and the gap between the
two cylinders is 0.12 cm. The inner cylinder is rotated at 200 rpm, and the torque is measured to
be 0.8 N-m. Determine the viscosity of the fluid.
Chapter II
1. The pressure difference between an oil pipe and a water pipe is measured by a double–fluid
manometer, as shown in the figure. For the given configuration and specific gravities, determine
the pressure difference ∆P = PB - PA.
2. A long, solid cylinder of radius 2 ft hinged at point A is used as an automatic gate, as shown in
the figure. When the water level reaches 15 ft, the cylindrical gate opens by turning about the
hinge at A. Determine a) the hydrostatic force acting on the cylinder and its line of action when
the gate opens and b) the weight of the cylinder per ft length of the cylinder.
3. The water in a 25 m deep reservoir is kept inside by a 150 m wide wall whose cross section is an
equilateral triangle, as shown. Determine a) the total hydrostatic force acting on the inner surface
of the wall and its line of action, b) the magnitude of the horizontal component of this force.
4. Consider a large cubic ice block floating in seawater. The specific gravities of ice and seawater
are 0.92 and 1.025, respectively. If a 10 cm high portion of the ice block extends above the
surface of the water, determine the height of the ice block below the surface.
5. The hull of a boat has a volume of 150 m3, and the total mass of the boat when empty is 8560 kg.
Determine how much load this boat can carry without sinking a) in a lake and b) in seawater with
a specific gravity of 1.03.