﻿ 流体力学代写-CHANICS 1|学霸联盟

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FLUID MECHANICS 1 (AMME2261/9261)
FINAL EXAMINATION

School of Aerospace, Mechanical and Mechatronic Engineering,
The University of Sydney

INSTRUCTIONS PROVIDED ON THE CANVAS EXAM SITE
CAREFULLY.

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SECTION A
You must show FULL working and ALL assumptions for all parts of all questions in
this section.

Question 1-Calculation based extension question [25 marks]

a) Fresh water flows down an inclined surface with a fully developed velocity profile as shown
in the figure below. It is known that the velocity has a parabolic form u=My2 + N.

The width (into the page) is b = 1 m and the height of the water flow is h = 30 mm. If the
volume flow rate is Q = 0.5 m3/s, then compute the values of M and N. [6 marks]

b) In part A, you considered the velocity profile of an unconfined flow. Now we will
consider a parabolic velocity profile with air in a confined pipe flow. Air enters a
circular pipe of radius R = 0.30m with a uniform velocity profile across the diameter.
The air exits the pipe as a fully developed flow with a parabolic velocity profile:

Figure 3.1: Air flow in a pipe.

For the case where umax = 8m/s, what is the velocity U at the pipe entrance? [6 marks]

.1)( 2
2
max ÷
÷
?
?
?
?
è
?
-=
R
ruru

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c) Now consider a two-dimensional flow that is steady and incompressible and is defined
by the general vector field below:

where and are unit vectors in the x and y directions of a Cartesian space,
respectively. Provide a valid y-direction velocity, if the x-direction velocity is given by
the equation below [4 marks]:

u=4y2 +8xy

How would your approach in determining the y-direction velocity change if the flow
were unsteady? What problems do you foresee when attempting to derive an
appropriate velocity field? [2 marks]

d) A laminar flow of oil flows through a narrow pipe that is inclined to the horizontal by
an angle θ. The pipe has a radius of R. The Reynolds number is given by Re. Derive
an expression for the pressure difference between the most elevated point in the pipe
(point “A”) and the exit of the pipe (point “B”), located downstream of point A. You
may assume that a length L, parallel to the pipe, separates points A and B. Your
expression for PB-PA must be in terms of the density and viscosity of the liquid,
gravitational acceleration g, the length of pipe, the angle θ, the radius R, and the
Reynolds number Re. Show all your working. [5 marks]

How would your approach change if you assumed the flow to be inviscid? Explain in
no more than 2 sentences and/or use equations as needed [2 marks]

jiuV
!!!
v+=
i
!
j
!

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Question 2-Long answer question [25 marks]

A liquid jet is impinging onto a flat surface. The jet is being issued from a fuel injector at a
particular velocity, before it impacts onto the solid flat surface. Derive all non-dimensional
numbers for the system using the Buckingham-pi theorem.

In your answer, consider the velocity of the liquid jet being ejected from the orifice of the
injector, consider the density of the liquid, the viscosity of the liquid, as well as 4 other
relevant physical parameters. [17 marks]

Briefly describe the physical meaning of each of the numbers you have derived [3 marks]

Explain how the non-dimensional numbers you have derived can help you design an
experiment to test how the injector works? [5 marks]

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Question 3-Long answer question [25 marks]

Starting from the full two-dimensional form of the differential conservation of momentum
equation, and making appropriate assumptions and simplifications, derive a FULLY
SIMPLIFIED algebraic expression that defines the velocity field close to the surface of a
smooth aircraft cruising at 10,000m above sea level. Show ALL of your steps and DO
NOT ignore viscosity. [20 marks]

In no more than 1 paragraph, comment on the velocity profile/velocity field you have
derived and its limitations in describing the actual velocity around an aircraft. In
commenting, you may wish to consider the assumptions you used and consider other
methods of coming up with a velocity field. [5 marks]

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SECTION B-

You MUST type your response to this question, it CANNOT be handwritten.
If you include equations/sketches, those portions can be hand drawn and then

Question 4-Open ended long response question [25 marks]

You are consulting for an engineering firm which is designing a new submarine. The
requirements of the submarine are for it to be easily maneuverable, operate in both salt
water and fresh water environments, and be rated to a depth of 500m.

Using as much knowledge from AMME2261/9261 as you can, suggest a series of initial
calculations/engineering design processes for the engineering firm to follow, so that they
can come up with some initial approximations for the size/shape/material (and any other
features you deem relevant) of the submarine. You MUST consider both the hydrostatic
and hydrodynamic requirements of the vessel in communicating with your clients.

Use sketches and equations as necessary, and state any assumptions embedded within the
design calculations or processes that you are suggesting.

A maximum of 2 pages is allowed (including equations/sketches)-anything beyond the 2pg
limit will NOT be marked.

[25 marks]

*****************END OF EXAM SCRIPT*****************

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