fluid practice problem

1. ENGR 2860U Practice Problems Page 1 of 3
ENGR 2860U: Fluid Mechanics
Practice Problems
1. Answering the following questions.
a. Identify the absolute and gauge pressures at Points 1 and 2 from the figure below.
b. The velocity vector for an incompressible, two-dimensional flow field is given below. The
velocity has units of metres per second, and x and y have units of metres. Determine the
angular rotation of a fluid element located at x = 0.3 m, y = 0.4 m.
= 5 − 8 ̂ + 2 + 3 ̂
c. There is steady laminar flow of water in a pipe of length, L. As the volume flowrate increases,
the pressure drop over the length, L … (1 mark)
i. …becomes larger ii. …becomes smaller
iii. …stays the same
2. A closed, pressurised tank contains two fluids which have separated into layers: water and a
hydrocarbon (specific gravity of 0.9). You know the air above the hydrocarbon layer is pressured to
5 kPa. A gauge at the bottom of the tank reads 30 kPa. Assuming there is enough water in the tank
to form a layer 35 cm deep, how thick is the hydrocarbon layer?
3. You are helping to design the water system for a new housing development north of UOIT. One of
your first tasks is to examine how water will get from the main pipes running down each street to
each individual house. For each house, a pipe of diameter 15 cm branches off from the main water
pipe in the street. That 15 cm-diameter pipe runs to a house, but once in the house the diameter is
reduced to 3 cm. In addition, the end of the 3 cm-diameter pipe is 1 m above the level of the 15 cm-
diameter pipe. If the developers want to achieve a flowrate of 0.003 m3
/s and a pressure of 100 kPa
at the end of the 3 cm-diameter pipe, what pressure is needed in the 15 cm-diameter pipe? Neglect
viscous effects for now.
Pressure(Pa)
100
90
80
70
Local atmospheric
pressure reference
Absolute zero reference
2
1

2. ENGR 2860U Practice Problems Page 2 of 3
4. The same development in Question 3 is thinking of incorporating a water tower: A large tank open
to the atmosphere, on tall supports, held high above the development. Water would be pumped
into the tank from a large reservoir nearby, and then could be used in case of emergency (e.g., a
drought). In this case, the tank is located 20 m (vertical) above the water level of the reservoir. You
estimate that the losses associated with pumping the water up to the reservoir are 50 N∙m/kg when
the flowrate is 0.005 m3
/s. How much power must the pump provide to make this system work?
5. As part of a fountain being designed for the centre of the housing development, water will flow as
two free jets from a tee attached to a pipe, as shown in the figure below. Your colleague who is in
charge of this segment of the design insists that the tee is properly attached to the pipe, but you are
not so sure. His design includes an anchoring force with an x-component of 80,000 N. Neglect
gravity and viscous effects.
i. Based on that anchoring force, what is the maximum allowable velocity of fluid leaving the tee?
Assume the velocity of each free jet is the same.
ii. Assume an exit velocity of 12 m/s in both the x- and y-directions (do not use your answer from
part i). What anchoring force is required in the y-direction for this system to work?
6. Hydraulic jumps commonly develop close to the end of a river spillway. In a hydraulic jump, the
depth of an open channel flow increases dramatically above ground level from an upstream value of
h1, to a downstream value of h2. The downstream depth h2 depends on the upstream depth, the
velocity of the fluid and the acceleration due to gravity. You have been asked to do some
experiments related to designing for hydraulic jumps. To simplify the process you first decide to
identify a suitable set of dimensionless variables for this problem. What are these variables?
7. You work for a big oil company at one of their refineries. As part of an expansion plan, you are
helping to design the piping system for transporting one of their products (motor oil) around the
plant (viscosity = 0.15 N∙s/m2
; density = 865 kg/m3
). You are focused on one section of pipe: It is 8 m
long, horizontal, has a diameter of 5 cm and has a volumetric flowrate of 0.01 m3
/s. What pressure
drop do you expect over this section?
8. As part of your work for the refinery, your boss has asked you to consider the large section of piping
required to transport the motor oil (viscosity = 0.15 N∙s/m2
; density = 865 kg/m3
) from the
distillation column (point A) to the storage tank (point B). The system uses galvanized iron piping,
15 cm in diameter, and you need to attain a flowrate of 0.09 m3
/s. The pressure in the pipe where it
Area = 0.2 m2
V (m/s)
V (m/s)
Area = 0.6 m2
Area = 0.8 m2

3. ENGR 2860U Practice Problems Page 3 of 3
leaves the distillation column (point A) is 20 kPa. The outlet to the storage tank (point B) is at 0 kPa
pressure, but is 3 m below point A in elevation. You know that to get from point A to point B, at a
minimum you will need to use three long radius 45° flanged elbows, two regular 90° flanged elbows,
and two fully open gate valves. Under these conditions, what length of straight pipe can you use in
the system?
9. You are assisting with the design of a new underwater turbine: It looks like a conventional wind
turbine, but will sit on the bottom of the ocean and be driven by currents. You are at the very early
stages of the design and doing some preliminary calculations. For convenience, you decide to treat
one turbine blade as a flat plate. To help plan your experiments, you want to know how thick the
boundary layer will be. Assume an upstream water velocity of 3 m/s, and a laminar boundary layer.
What is the thickness of the boundary layer at a distance of 0.5 m from the leading edge of your
prototype blade?
ENGR 2860U Practice Problems 29Nov14.docx