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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 Âµ 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
liquidâ€™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
Reynoldâ€™s number) that combines velocity V, system size L,

fluid density Ï and surface tension Ïƒ is

(a) LÏÏƒ/V,

(b) ÏVL2/Ïƒ,

(c) ÏÏƒV2/L,

(d) ÏƒLV2/Ï,

(e) ÏLV2/Ïƒ. 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 oceanâ€™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
jetâ€™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

turbineâ€™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 turbineâ€™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

streamtubeâ€™s entry plane as shown in Figure b).

(c) Both of the above statements could be true depending on
the diameter of the turbineâ€™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
tankâ€™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: ___________________

(a)

(b)

(c)

(d)

(e) 10 kg/s,

1.0 kg/s,

0.12 kg/s,

0.012 kg/s.

Impossible to determine without information about the
tankâ€™s radius. Section 2: Questions (Full solution required).

Please provide your answers on separate pages. Question 13

A viscous fluid (with a specific weight Î³f = 1280 [kg/m3]
and viscosity Î¼f = 0.15 [kgâ‹…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 âˆ†p = p1

â€“ 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

Î”

+

âˆ™ ( ) âˆ™ (2 2 âˆ’ 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

â€œBefore I die, I hope someone will clarify quantum physics
for me. After I die, I hope God will explain turbulence

to me.â€[1]

Obviously, if a Nobel prize-winning physicist found the
phenomenon of turbulence difficult to understand, then

you may also expect some difficulties â€¦ however, this
doesnâ€™t mean that you cannot have some insight into this

intriguing phenomenon.

[1] Giles Foden, â€œTurbulence,â€ 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
â€œhâ€ is the depth of the water in the tank, and â€œgâ€ 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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