Chapter 3, Fundamentals of Inviscid, Incompressible Flow Video Solutions, Fundamentals of Aerodynamics

Problem 1

For an irrotational now, show that Bernoulli's equation holds between any points in the flow, not just along a streamline.

Narayan Hari

Numerade Educator

03:10

Consiler a venturi with a throat-to-inlet area ratio of 0.8 . mounted on the side of an airplane fusclage. The airplane is in flight at standard sea level. If the static pressure at the throat is $2100 \mathrm{tb} / \mathrm{ft}^2$. calculate the velocity of the airplane.

Narayan Hari

Numerade Educator

03:24

Problem 3

Cnnsider a venturi with a small hole drilled in the side of the throat. This hole is connected via a tube to a closed reservoir. The purpose of the venturi is to create a vacuum in the reservoir when the venturi is placed in an airstream. (The rncunun is defined as the pressure difference helow the outside ambient pressure.) The venturi has a throat-10-inlet area ratio of 0.85 . Calculate the maximum vacuum obainable in the reservoir when the venturi is placed in an airstream of $90 \mathrm{~m} / \mathrm{s}$ at standard sea level conditions.

Ma Ednelyn Lim

Numerade Educator

01:00

Problem 4

Consider a low-speed open-circuit subsonic wind tunnel with an inlet-to-throat area ratio of 12. The tunnel is turned on, and the pressure difference between the inlet (the settling chamber) and the test section is read as a height difference of $10 \mathrm{~cm}$ on a U-tube mercury manometer. (The density of liquid mercury is 1.36 $\times 10^{+} \mathrm{kg} / \mathrm{m}$ '.) Calculate the velocity of the air in the test section.

Kratika Bhadauria

Numerade Educator

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Problem 5

Assume that a Pitot tube is inserted into the test-section flow of the wind tunnel in Prob. 3.4. The tunnel test section is completely sealed from the outside ambiem pressure. Calculate the pressure measured by the Pinto tube, assuming the static pressure at the tunnel inlet is atmospheric.

Victor Salazar

Numerade Educator

00:49

Problem 6

A Pitol tube on an airplane flying at standard sea level reads $1.07 \times 10^4 \mathrm{~N} / \mathrm{m}^2$. What is the velocity of the airplane?

Julie Silva

Numerade Educator

02:53

Problem 7

At a given point on the sufface of the wing of the airplane in Prob. 3.6 , the flow velocity is $130 \mathrm{~m} / \mathrm{s}$. Calculate the prescure cocfficient as this point.

Guilherme Barros

Numerade Educator

07:59

Problem 8

Consider a uniform flow with velocity $V_*$. Show that this flow is a physically possible incompressible flow and that it is irmetational.

Khoobchandra Agrawal

Numerade Educator

Problem 9

Show that a source flow is a physically possible incompressible flow everywhere except at the origin. Also show that it is irrotational everywhere.

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01:32

Problem 10

Prove that the velocity potential and the stream function for a uniform flow, Eqs. (3.53) and (3.55). respectively, satisfy Laplace's equation.

Penny Riley

Numerade Educator

01:32

Problem 11

Prove that the velocity potential and the stream function for a source flow. Eqs. (3.67) and (3.72). respectively, satisfy Laplace's equation.

Penny Riley

Numerade Educator

08:19

Problem 12

Consider the flow over a semi-infinite hody as discussed in Sec. 3.11. If $V_{\mathrm{x}}$ is the velocity of the uniform stream. and the stagnation point is $1 \mathrm{ft}$ upstream of the source:
(a) Draw the resulting scmi-infinite body to scale on graph paper.
(b) Plot the pressure cnefficient distribution over the body; i.e., plot $C_r$ versus distance along the centerline of the body.

Khoobchandra Agrawal

Numerade Educator

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Problem 13

Derive Eq. (3.81). Hint: Make use of the symmetry of the flow field shown in Fig. 3, I6, i.e., start with the knowledge that the stagnation points must lie on the axis aligned with the direction of $V_{\mathrm{a}}$.

Victor Salazar

Numerade Educator

01:56

Problem 14

Derive the velocity potential for a doublet: i.e., derive Eq. (3.88). Hint; The easiest method is to start with Eq. (3.87) for the stream function and extract the velocity potential.

James Kiss

Numerade Educator

05:30

Problem 15

Consider the nonlifting flow over a circular cylinder. Derive an expression for the pressure coefficient at an arbitrary point $(r, \theta)$ in this flow, and show that it reduces to Eq. (3.101) on the surface of the cylinder.

Satpal Satpal

Numerade Educator

02:12

Problem 16

Consider the nonlifting flow over a circular cylinder of a given radius, where $V_{\mathrm{v}}=20 \mathrm{ft} / \mathrm{s}$. If $V_{\mathrm{x}}$ is doubled, that is, $V_*=40 \mathrm{ft} / \mathrm{s}$, does the shape of the streanlines change? Explain.

Jack Poling

Numerade Educator

03:29

Problem 17

Consider the lifting flow over a circular cylinder of a given radius and with a given circulation. If $V$, is doubled, keeping the circulation the same, docs the shape of the streamlines change? Explain.

Ma Ednelyn Lim

Numerade Educator

01:40

Problem 18

The lift on a spinning cireular cylinder in a frec stream with a velocity of $30 \mathrm{~m} / \mathrm{s}$ and at standard sea level conditions is $6 \mathrm{~N} / \mathrm{m}$ of span. Calculate the circulation around the cylinder.

Chai Santi

Numerade Educator

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