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NAME: __________________________________________ STUDENT NUMBER: ___________________
Section 1: Multiple Choice Questions (Brief explanation required).
Please briefly explain your answers on separate pages.
Question 1
The dynamic viscosity µ of any liquid is primarily a function of
(a) Density,
(b) Temperature,
(c) Pressure,
(d) Velocity,
(e) Surface tension. Question 2
When a fluid moves past a solid, stationary wall, the speed of the fluid changes with distance from the solid wall.
However, the fluid adjacent to the wall is also stationary. This condition is known as:
(a) The stationary condition,
(b) The no slide condition,
(c) The no slip condition,
(d) The no shear stress condition,
(e) The solid wall principle of flow. Question 3
An incompressible fluid is defined as:
(a) A fluid in which the pressure is constant everywhere in the fluid,
(b) A fluid in which density is constant everywhere in the fluid,
(c) A fluid in which the pressure at a point does not change with time,
(d) A fluid in which the density at a point does not change with time,
(e) Both (b) and (d). Question 4
To employ the control volume approach we need to know:
(a) Fluid properties (such as pressure, density and velocity) at every point inside the control volume,
(b) Fluid properties (such as pressure, density and velocity) at every point on the control surface alone
and we do not need to know these fluid properties inside the control volume,
(c) Fluid properties (such as pressure, density and velocity) at every point inside the control volume and
at every point on the control surface. Question 5
The specific gravity of mercury at 80oC is 13.4. This liquid’s specific weight at this temperature is
(a) 13.4 kN/m3,
(b) 13.4 x 103 kN/m3,
(c) 134 kN/m3,
(d) 1.34 kN/m3. 3 NAME: __________________________________________ STUDENT NUMBER: ___________________ Question 6
The only possible dimensionless group (i.e. like the Reynold’s number) that combines velocity V, system size L,
fluid density ρ and surface tension σ is
(a) Lρσ/V,
(b) ρVL2/σ,
(c) ρσV2/L,
(d) σLV2/ρ,
(e) ρLV2/σ. Question 7
If the density of air increases by a factor of 1.25 (i.e. the density increases by 25%) as a result of a temperature
change, then the specific weight
(a) Increases by a factor of 1.25,
(b) Increases by a factor of 14.2,
(c) Decreases by a factor of 1.25,
(d) Decreases by a factor of 14.2,
(e) Remains unchanged. Question 8
A gauge is attached to a pressurized tank of nitrogen gas and reads a gauge pressure of 28 inches of mercury. If
atmospheric pressure 14.4 psi (absolute), then what is the absolute pressure inside the nitrogen tank?
(a) 194 kPa,
(b) 99 kPa,
(c) 101 kPa,
(d) 203 kPa,
(e) 95 kPa. Question 9
On a sea-level standard day, a pressure gauge held below the surface of the ocean (ocean water SG is 1.025),
reads an absolute pressure of 1.4 MPa (abs). How far below the ocean’s surface is this pressure gauge?
(a) 133 m,
(b) 4 m,
(c) 129 m,
(d) 2080 m,
(e) 140 m. Question 10
A jet of water that is 3 cm in diameter strikes normal to a plate as shown in the figure below. If the force required
to hold the plate stationary is 23 N, then what is the jet’s speed?
(a) 4.0 m/s,
(b) 23.0 m/s, 4 NAME: __________________________________________ STUDENT NUMBER: ___________________
(c) 2.85 m/s,
(d) 5.7 m/s,
(e) 8.1 m/s. Question 11
An example of the wake generated by a wind turbine is sketched in the figures shown below. If this wake can be
assumed to be confined by a streamtube, and if the air at these low speeds can be assumed to be incompressible,
then which of the following statement is true?
(a) Only those air particles which entered the streamtube through area A1 will pass through the wind
turbine’s rotor disc (A); shown as the shaded area in Figure a).
(b) Since conservation of mass must be maintained, particles passing through the wind turbine’s rotor
disc (A) must enter through an area A2 that is equal to A (that is, A2 = A where A2 is located at the
streamtube’s entry plane as shown in Figure b).
(c) Both of the above statements could be true depending on the diameter of the turbine’s rotor disc. Question 12
The cylindrical tank sketched below has two connecting pipes of equal radius, R. The lower pipe provides water
inflow while the second pipe is used for air outflow. The pressure inside the tank, above the water surface, is equal
to one atmosphere. The height of the tank is 50R but the tank’s radius is unknown. If the tank is half full and the
water mass inflow is 10 kg/s, then the air mass outflow will be approximately 5 NAME: __________________________________________ STUDENT NUMBER: ___________________
(e) 10 kg/s,
1.0 kg/s,
0.12 kg/s,
0.012 kg/s.
Impossible to determine without information about the tank’s radius. Section 2: Questions (Full solution required).
Please provide your answers on separate pages. Question 13
A viscous fluid (with a specific weight γf = 1280 [kg/m3] and viscosity μf = 0.15 [kg⋅s/m2] ) is contained between
two infinite, horizontal parallel plates as shown in the sketch below. The fluid moves between these parallel
plates under the action of a pressure gradient and the upper plate moves with a velocity U while the bottom plate
is fixed. A U-tube manometer connected between two points along the bottom indicates a differential height
reading of h = 2.5 [mm].
(a) Determine the pressure drop between the two points (1) and (2) on the lower plate; that is, evaluate ∆p = p1
– p2.
(b) If the upper plate moves with a velocity of 6 mm/s, then what is the shear stress on the fixed plate if the fluid
velocity profile between the plates is given by
() = 2
∙ ( ) ∙ (2 2 − 3 )
2 3 where u is the fluid speed in the horizontal direction between the plates, b is the vertical distance between
the two plates and L is the horizontal distance between point (1) and (2).
(c) What is the shear stress at the mid-point between the plates? 6 NAME: __________________________________________ STUDENT NUMBER: ___________________ Question 14
Frequently fluid flow phenomenon are described by two terms: laminar and turbulent. For this question you are
asked to provide (in no more than three pages) an introductory explanation of the phenomenon of turbulence
and how turbulent flow is quantitatively characterized.
You are encouraged to use outside (of class) sources of information, however you MUST reference the source(s)
of your information to assign appropriate credit to the source(s). If it is discovered that you have used and not
attributed any source of information in your answer, then you may fail this question and receive a mark of zero.
For example, on the back fly cover of one popular novel the author quotes A. Einstein has been quoted as saying
“Before I die, I hope someone will clarify quantum physics for me. After I die, I hope God will explain turbulence
to me.”[1]
Obviously, if a Nobel prize-winning physicist found the phenomenon of turbulence difficult to understand, then
you may also expect some difficulties … however, this doesn’t mean that you cannot have some insight into this
intriguing phenomenon.
[1] Giles Foden, “Turbulence,” Faber & Faber, London (2009), as quoted on back cover. Question 15
The sketch below shows a 1.5 m diameter tank being filled from an overhead pipe with room-temperature water
at the rate of 175 litres/s through its top. The diameter of this overhead inflow pipe is 30 cm. At the same time,
water is draining from the bottom of the tank through two small pipes of 10 cm and 15 cm in diameter,
respectively. If we assume that the speed of the water outflow from both drainage pipes (at the bottom of the
tank) can be calculated from relation v = (2gh)1/2 , where “h” is the depth of the water in the tank, and “g” is the
gravitational acceleration ( g=9.81m/s2 ), then answer the following: 7 NAME: __________________________________________ STUDENT NUMBER: ___________________ (a) When the volume of the water in the tank reaches 300 litres, then what would be the rate of change of the
water level inside the tank?
(b) How much water (in litres) has been accumulated in the tank by the time the steady state condition is reached
(i.e. when the water level would remain unchanged)? Question 16
Water enters and flows through the angled pipe sketched below. The pipe discharges at atmospheric pressure.
It was determined that the axial forces exerted at the rods (A and B) holding the pipe stationary are,
respectively, 132 N and 62.3 N. Neglecting viscous effects, the weight of the water inside the pipe and
assuming uniform velocity profiles at the inflow and exit sections, calculate
(a) The volume flow rate through this pipe, and
(b) The gauge pressure at the inflow cross-section.
You may assume that the specific weight of the water is 9810 N/m3 and acceleration of gravity is 9.81 m/s2. 8


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