Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 3, Problem 3.15P
Consider the nonlifting flow over a circular cylinder. Derive an expression for the pressure coefficient at an arbitriry point
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4. Fluid flows axially in the annular space between a cylinder and a concentric rod. The radius of the rod is
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Chapter 3 Solutions
Fundamentals of Aerodynamics
Ch. 3 - For an irrotational flow. show that Bernoullis...Ch. 3 - Consider a venturi with a throat-to-inlet area...Ch. 3 - Consider a venturi with a small hole drilled in...Ch. 3 - Consider a low-speed open-circuit subsonic wind...Ch. 3 - Assume that a Pitot tube is inserted into the...Ch. 3 - A Pilot tube on an airplane flying at standard sea...Ch. 3 - At a given point on the surface of the wing of the...Ch. 3 - Consider a uniform flow with velocity V. Show that...Ch. 3 - Show that a source flow is a physically possible...Ch. 3 - Prove that the velocity potential and the stream...
Ch. 3 - Prove that the velocity potential and the stream...Ch. 3 - Consider the flow over a semi-infinite body as...Ch. 3 - Derive Equation (3.81). Hint: Make use of the...Ch. 3 - Derive the velocity potential for a doublet; that...Ch. 3 - Consider the nonlifting flow over a circular...Ch. 3 - Consider the nonlifting flow over a circular...Ch. 3 - Consider the lifting flow over a circular cylinder...Ch. 3 - The lift on a spinning circular cylinder in a...Ch. 3 - A typical World War I biplane fighter (such as the...Ch. 3 - The Kutta-Joukowski theorem, Equation (3.140), was...Ch. 3 - Consider the streamlines over a circular cylinder...Ch. 3 - Consider the flow field over a circular cylinder...Ch. 3 - Prove that the flow field specified in Example 2.1...
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- 3. The velocity components in a two dimensional flow field for an incompressible fluid are expressed as u = 2y -. v = xy? – 2y - 3' (a) Show that these functions represents a possible case of an irrotational flow, (b) obtain an expression for the stream function y and (c) obtain an expression for the velocity potential o.arrow_forward(c) A flow field consists of two free vortices which are rotating in clockwise direction with the strengths, K of 20 m²/s and 15 m/s located at points A(3, 3) and B(-4,-4) respectively. Sketch the whole flow field and indicate all the points (A, B, C and stagnation (i) point(s), note that point C (-4,0) is given in part (iii)) and velocities involved clearly. (ii) Find the stagnation point or points of this flow field and indicate the coordinate or coordinates clearly. (iii) Find the resultant velocity (both magnitude and angle with x-axis) at point C(-4, 0). K Note: For free vortex, the velocity components are v, = 0 and v, ==. rarrow_forwardthis is not simple couette flow! the walls on the side have an effect on the velocity profile, but im not sure how. 1. Consider a two-dimensional rectangular region which is very long and narrow, and filled with a fluid. Along one of the long walls is a conveyor belt, which moves with constant velocity U. Near the center of the region, far from the ends, the flow may be assumed to be parallel flow. Find U(y).arrow_forward
- Thevelocity components in thex and y directions are given by u = Ary3 – x²y, v = xy? -÷y*. The value of 1 for a possible flow field involving an incompressible fluid isarrow_forwardConsider a wing in a high-speed wind tunnel. At a point on the wing, the velocity is 850 ft/s. If the test-section flow is at a velocity of 780 ft/s, with a pressure and temperature of 1 atm and 505°R, respectively, calculate the pressure coefficient at the point. detailed solution plsarrow_forwardOne dimensional flow occurs in the circular tube at the location adequately far from the entrance shown in the figure right. Velocity profile is the laminar and expressed as; U(x) = Uman(1-r³/R?) Where R: radius of the tube, r: distance beginning from the center and Umas: maximum velocity (at the center). Drive the expression for the drag force per unit area applied to both plates by the fluid (F/A). If the drag force is 0.565 N, calculate the necessary velocity for the water at 20°C flow through the tube with the radius of 0.08 m and 15 m length (u:0.0010 kg/m. s). - Umaxarrow_forward
- The velocity components in the x and y directions are given by 3 u = Axy3 - x2y, v = xy2 -- The value of a for a possible flow field involving an incompressible fluid isarrow_forwardOne dimensional flow occurs in the circular tube at the location adequately far from the entrance shown in the figure right. Velocity profile is the laminar and expressed as; U(x) = Umax (1-r/R?) Where R: radius of the tube, r: distance beginning from the center and Umax : maximum velocity (at the center). Drive the expression for the drag force per unit area applied to both plates by the flu id (F/A). If the drag force is 0.565 N, calculate the necessary velocity for the water at 20°C flow through the tube with the radius of 0.08 m and 15 m length (u:0.0010 kg/m. s). R -Umaxarrow_forwardConsider a fluid element in the flow shown in the figure. Explain if the fluid elements A and B would rotate or not. Why? Aarrow_forward
- For fully-developed laminar flow through a pipe with ra- dius R, the fluid velocity is very accurately modeled as V = (Ur, Up, U₂) = (0,0, uz), with the axial component of velocity given by Ө where ue is the fluid speed at the center of the pipe, r = 0). Compare the momentum flux for the laminar flow velocity distribution, uz (r), with that for a uniform flow having (constant) speed uave = uc/2, recalling that the momentum flux through a control surface is given by U₂(7) = uc [1 − (77)²], z MF √ PV (V - ñ) dA. Answer: |MF|lam = |MF|avearrow_forwardFind the resultant force in the y-direction Fr,y for a volumetric flow rate in the y direction of 100 L/hr, a pressure of 150 kPa, and a diameter of 3 cm. Use the equation Fr, y = -m1y1 - P1A1arrow_forwardThe velocity components of a flow field are given in polar coordinates: q, = r² cos 0 and qo = –3r² sin 0 Please enter the number of stagnation points that are located in the flow field?arrow_forward
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