AE220 Aerodynamics I
Midterm Exam
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Date: Oct. 18 (Mon), 1:00~4:00 pm
Place: ZOOM
The exam is a closed-book test
Total score = 100%
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Section A
[True/false questions]
Total 10 questions (Each is worth 3% => total 30%)
(A.1)
The term uniform flow-field is used to describe a flow in which the velocity is constant, i.e., independent
of all space coordinates, throughout the entire flow-field.
a) true
b) false
(A.2)
Fluids such as water and gasoline are non-Newtonian under normal conditions.
a) true
b) false
(A.3)
The barometer readings should be made at the level of the middle of the meniscus. This is away from
the minimum effects of surface tension and thus nearest to the proper liquid level.
a) true
b) false
(A.4)
In a static fluid, there are shear stresses.
a) true
b) false
(A.5)
The sensitivity of a manometer is a measure of how sensitive it is compared to a simple water filled Utube manometer.
a) true
b) false
(A.6)
The line of action of the buoyancy force, acts through the centroid of the displaced volume.
a) true
b) false
Page 1 of 3
(A.7)
In a static, homogeneous fluid, a fluid particle retains its identity for all time, and fluid elements do not
deform.
a) true
b) false
(A.8)
Streamlines are lines drawn in the flow-field so that at a given instant they are normal to the direction
of flow at every point in the flow-field.
a) true
b) false
(A.9)
In differential control volume analysis, because the control volume is bounded by streamlines, flow
along the bounding surfaces occurs only at the end sections.
a) true
b) false
(A.10)
The Bernoulli equation is subject to the following restrictions: steady flow, no friction, flow along a
streamline, compressible flow.
a) true
b) false
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Section B
[Conceptual questions]
Total 3 questions (Each is worth 10% => total 30%)
(B.1)
Under what circumstances can a fluid be treated as a continuum, for which, by definition, properties
vary smoothly from point to point? Explain along with relevant sketches and/or illustrations.
(B.2)
In a steady flow, why pathlines, streaklines, and streamlines are identical lines in the flow-field? Explain
along with relevant sketches and/or illustrations.
(B.3)
Let’s look at the relation of system derivatives to the control volume (CV) formulation below,
Discuss the meaning of each term of the equation. What is the difference in the meaning between the
three terms? What is the difference between the system and the control volume?
Page 2 of 3
Section C
[Problem-solving questions]
Total 3 questions (Each is worth 13, 13, 14% => total 40%)
(C.1) (13%)
A curved surface is formed as a quarter of a circular cylinder with R = 0.75 m as shown. The surface is
w = 3.55 m wide. Water stands to the right of the curved surface to depth H = 0.65 m. Calculate the
vertical hydrostatic force on the curved surface. Evaluate the line of action of this force. Find the
magnitude and line of action of the horizontal force on the surface.
(C.2) (13%)
A plane jet of water strikes a splitter vane and divides into two flat streams, as shown in the diagram.
Find the mass flow rate ratio, m̊2/m̊3, required to produce zero net vertical force on the splitter vane. If
there is a resistive force of 16 N applied to the splitter vane, find the steady speed U of the vane.
(C.3) (14%)
A small cart that carries a single turning vane rolls on a level track. The cart mass is M = 5 kg and its
initial speed is U0 = 5 m/s. At t = 0 s, the vane is struck by an opposing jet of water, as shown. Neglect
any external forces due to air or rolling resistance. Determine the jet speed V required to bring the cart
to rest in (a) 1 s and (b) 2 s. In each case find the total distance traveled.
Page 3 of 3
Formula Sheet (Governing Equations)
Constant
𝜌𝑤𝑎𝑡𝑒𝑟 = 999 𝑘𝑔⁄𝑚3
𝑔 = 9.81 m/𝑠 2
Problem (C.1)
I𝑋𝑋 =
𝑤 ∙ 𝐻3
12
Problem (C.2)
(Momentum equation)
Problem (C.3)
(Momentum equation)