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MA2003 INTRODUCTION TO THERMO-FLUIDS Tutorial 7 Fluid
Properties, pressure and manometers
1. Two layers of fluid are dragged along by the motion of an
upper plate as shown in Figure 1 with the bottom plate remains
stationary. Determine the ratio of shear stress on upper plate to
that of lower plate.
Figure 1 Figure 2
2. An inverted 0.1-m-diameter cylinder is partially filled with
water and covered by a plate as shown in Figure 2. A force of 20 N
is needed to pull the plate away from the cylinder. Determine the
air pressure inside the cylinder. Neglect the mass of the
plate.
3. Determine the elevation difference, h, between the water
levels in the two open
tanks in Figure 3.
Figure 3 Figure 4 4. Determine the density of the unknown liquid
occupied the lower half of the tank
(Figure 4). Ans: 1. [1]; 2. [-4.51 kPa]; 3. [0.04 m]; 4. [1930
kg/m3].
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MA2003 INTRODUCTION TO THERMO-FLUIDS Tutorial 8 Manometers,
hydrostatic forces
1. Please refer to the figure below. Determine the pressure in
pipe B when the pressure
in pipe A is -30mm Hg gauge.(S.G of mercury 13.6 and S.G. of oil
0.7). 2. A gate with the shape as shown in Figure 2 is mounted on a
horizontal shaft.
Determine the net moment about the shaft from the hydrostatic
forces acting on the gate.
Figure 2 Figure 3 3. Calculate the horizontal and vertical
hydrostatic forces acting on the dam shown in
Figure 3 and hence determine the minimum coefficient of friction
needed to prevent sliding. Specific weight of concrete is 23.6
kN/m3. Width of the dam is 1 m.
4. A cylindrical tank with its axis horizontal has a diameter of
2.0 m and a length 4.0 m.
The ends of the tank are hemispherical. A vertical,
0.1-m-diameter pipe is connected to the top of the tank. The tank
and the pipe are filled with ethyl alcohol (S.G. = 0.79) to a level
of 1.5 m above the top of the tank. Determine the horizontal force
of alcohol on one of the curved ends.
Ans: 1. [34.3 kPa]; 2. [750 kNm]; 3. [78.4 kN, 62.8 kN, 0.147];
4. [60.8 kN].
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10 m
300 300
d
Water
Water surface
MA2003 INTRODUCTION TO THERMO-FLUIDS Tutorial 9 Hydrostatic
forces, stability, and rigid body motion
1. A conical plug is placed at the bottom of a tank filled with
a liquid of specific weight
27 kN/m3 (Figure 1). The air space is pressurized to 50 kPa.
Determine the magnitude, dirction and line of action of the force
on the curved surface of the cone.
Figure 1 Figure 2 2. A 20-m-long wooden barge has a triangular
cross-section as shown in Figure 2. The
barge is submerged to a depth d in the water. Determine the
value of d, given that the specific gravity of wood is 0.65. By
means of calculations, state whether the barge is stable or
not.
3. An open rectangular tank 1m wide and 2 m long contains
gasoline to a depth of 1m. If
the height of the tank sides is 1.5 m, what is the maximum
horizontal acceleration (along the longitudinal axis) that can
develop before the gasoline would begin to spill?
4. The U-tube contains mercury and rotates about the off-center
axis a-a. At rest the
depth of mercury in each leg is 150mm. Determine the angular
velocity for which the difference in heights between the two legs
is 75mm.
Ans: 1. [128 kN]; 2. [2.33 m, stable]; 3. [4.91 m/s2]; 4. [6.04
rad/s]
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MA2003 INTRODUCTION TO THERMO-FLUIDS Tutorial 10 Bernoulli
equation
1. Water flows through a pipe reducer as shown. Determine the
flow rate, Q, if the
diameter of the smaller pipe D = 0.05m. What would be the flow
rate if gasoline is the working fluid?
2. Water of constant depth h flows from a large tank through
three pipes of different diameters and inclinations as shown in
Fig. 2. Viscous effects are negligible. Determine heights h1, h2
and h3 in terms of h to which the three streams rise.
Figure 2 Figure 3 3. As shown in Fig. 3, determine the height,
h, and the pressure inside the horizontal
pipe when the nozzle exit is at the same level as the oil/water
interface. Assume ideal flow.
4. Determine the water depth in the upper tank, hA, when the
flow reaches a steady condition (i.e. constant water levels in both
tanks). Assume frictionless flow.
Ans: 1. [0.0156 m3/s]; 2. [h, h, and 0.5h]; 3. [2.8 m and 35.5
kPa]; 4. [15.4 m]
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MA2003 INTRODUCTION TO THERMO-FLUIDS Tutorial 11 Mass
conservation
1. Oil having a specific gravity of 0.9 is pumped as shown to
mix with water as shown
in Figure 1. The water flow rate is 2 m3/s. The water and oil
mixture has an average specific gravity of 0.95. Calculate the
flowrate of oil.
Figure 1 Figure 2 2. A hypodermic syringe is used to apply a
vaccine as shown in Figure 2. If the plunger
is moved forward at a steady rate of 20 mm/s and if vaccine
leaks past the plunger at 0.1 of the volume flowrate out of the
needle opening, calculate the average velocity of the needle exit
flow. The inside diameters of the syringe and needle are 20 mm and
0.7 mm.
3. Oil (SG = 0.9) flows downward through a vertical pipe
contraction as shown. If the mercury manometer reading, h = 100 mm,
determine the volume flowrate for frictionless flow. Is the actual
flowrate more or less than the frictionless value? Explain.
Figure 3 Figure 4 4. Estimate the time required to fill with
water a cone-shaped container shown in Figure
4 if the filling rate is 76 Liter/min.
Ans: 1. [2.0 m3/s]; 2. [14.8 m/s]; 3. [0.042 m3/s]; 4. [11.6
min]
1.5 m
1.5 m