Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 1, Problem 1.20P
Consider the existence of a forward-facing axial aerodynamic force on an airfoil, as discussed in Section 1.16. Can a forward-facing axial force exist on a flat plate at an angle of attack in a flow? Thoroughly explain your answer.
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You are designing an airfoil for a new hobby RC plane. Because of your limited knowledge, you have mistakenly approximated your airfoil as an ellipse with a = 75mm and b = 12mm. Here, “a” is the depth of your wing and “b” is the thickness. Your plane travels through the air at approximately 20mph (8.9m/s). As it does so, skin friction produces a drag-induced heat of 800W on your wind, of length 1m.
Properties of Air: k = 0.025 W/mK, Pr = 0.72, v = 1.847 x 10−5, u = 16.84 x 10−6, p = 1.2 kg/m3, B = 1/Tf (ideal gas), TInfinity = 25oC
a) What is the Reynold’s number? Hint: “D” is taken to be the thickness for an elliptical crosssection.
b) What is the Nusselt number?
c) What is the convection coefficient?
d) What is the average temperature of your wing? Assume an ellipse perimeter of approximately 200mm.
You are designing an airfoil for a new hobby RC plane. Because of your limited knowledge, you have mistakenly approximated your airfoil as an ellipse with a = 75mm and b = 12mm. Here, “a” is the depth of your wing and “b” is the thickness. Your plane travels through the air at approximately 20mph (8.9m/s). As it does so, skin friction produces a drag-induced heat of 800W on your wind, of length 1m.
Properties of Air: k = 0.025 W/mK, Pr = 0.72, v = 1.847 x 10−5, u = 16.84 x 10−6, p = 1.2 kg/m3, B = 1/Tf (ideal gas), TInfinity = 25oC
a) What is the average temperature of your wing? Assume an ellipse perimeter of approximately 200mm.
Chapter 1 Solutions
Fundamentals of Aerodynamics
Ch. 1 - For most gases at standard or near standard...Ch. 1 - Starting with Equations (1.7),(1.8), and (1.11),...Ch. 1 - Consider an infinitely thin flat plate of chord c...Ch. 1 - Consider an infinitely thin flat plate with a 1 m...Ch. 1 - Consider an airfoil at 12 angle of attack. The...Ch. 1 - Consider an NACA 2412 airfoil (the meaning of the...Ch. 1 - The drag on the hull of a ship depends in part on...Ch. 1 - The shock waves on a vehicle in supersonic flight...Ch. 1 - Consider two different flows over geometrically...Ch. 1 - Consider a Lear jet flying at a velocity of 250...
Ch. 1 - A U-tube mercury manometer is used to measure the...Ch. 1 - The German Zeppeins of World War I were dirigibles...Ch. 1 - Consider a circular cylinder in a hypersonic flow,...Ch. 1 - Derive Archimedes principle using a body of...Ch. 1 - Consider a light, single-engine, propeller-driven...Ch. 1 - Consider a flat plate at zero angle of attack in a...Ch. 1 - Consider the Space Shuttle during its atmospheric...Ch. 1 - The purpose of this problem is to give you a feel...Ch. 1 - For the design of their gliders in 1900 and 1901,...Ch. 1 - Consider the existence of a forward-facing axial...
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- Use the result of Problem 3 and find the y-component of velocity over the plate of Problem 6 at the outer edge of the boundary layer for two locations; a) the middle of the plate and b) the trailing edge of the plate. Problem 1 Start with Equation IVb.2.7 (see attached image) and obtain an approximate relation for the thickness of the hydrodynamic boundary layer. Problem 3 Assume a two-dimensional flow over a flat plate. Use the result of Problem 1 for the thickness of the boundary layer and the velocity profile for Vx, as given by Equation IVb.2.1 (see attached image) and obtain a relation for Vy. [Hint: Use the equation for continuity given by Equation IIIa.3.13-1 (see attached image)]. Problem 6 Air at atmospheric pressure and room temperature (27 C) flows over a flat plate at a speed of 2 m/s. The length of the plate is 0.5 m. Find the thickness of the boundary layer at the middle of the plate (x = 25 cm) and at the trailing edge (x = L).arrow_forwardCurrent Attempt in Progress In the 1930s, the U.S. Navy operated dirigibles. The largest was the U.S.S. Akron with a length of 785 ft and a maximum diameter of 132 ft. Its maximum speed was 84 mph (123.2 ft/sec). Moving at top speed at 10,000 ft standard atmosphere, estimate the power required in horsepower to overcome the friction drag. Disregard effects of fins and other protrusions. Assume the surface of the dirigible is smooth and the friction drag is that over a flat plate. (Hint: "unwrap" the outer surface of the ship.) W = hparrow_forwardThe lift on a spinning circular cylinder in a freestream with a velocity of 22 m/s and at standard sea level conditions is 6 N/m of span. Calculate the circulation around the cylinder.arrow_forward
- In the experiment of high Reynolds number, an airfoil of width, W= 30 cm, and chord length, C = 24 cm is subjected to airflow at 1 atm and 5 °C as shown in Figure 2.1. The airfoil can be approximated as a flat plate. The total drag force acting on the airfoil is 40.2 N. The pressure drag acting on the airfoil is measured to be 39.9 N by using pressure sensors throughout the surface. Given, the drag coefficient of the airfoil is Cp = 0.04, the density and kinematic viscosity of air at 1 atm and 5 °C is 1.269 kg/m³ and 1.382 x 10$ m²/s, respectively. i. Determine the friction drag coefficient of the airfoil. ii. Verify that the boundary layer flow at the trailing edge is turbulent. V C Figure 2.1 The airflow on a streamlined bodyarrow_forward4.18 A flat plate is immersed in a Mach 2 flow at standard sea level conditions at an angle of attack of 2°. Assuming the same shear stress distribution given in Example 1.8, calculate, per unit span: (a) lift, (b) wave drag, and (c) skin friction drag. What percentage of the total drag is skin-friction drag? Compare this percentage with the 10° angle of attack case discussed in Example 1.8.arrow_forwardIcebergs can be driven at substantial speeds by the wind.Let the iceberg be idealized as a large, flat cylinder, D >> L,with one-eighth of its bulk exposed, as in Fig.. Letthe seawater be at rest. If the upper and lower drag forcesdepend on relative velocities between the iceberg and thefluid, derive an approximate expression for the steady icebergspeed V when driven by wind velocity U.arrow_forward
- Assume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2 (2116 lb/ft2), respectively. The lift on a spinning circular cylinder in a freestream with a velocity of30 m/s and at standard sea level conditions is 6 N/m of span. Calculate thecirculation around the cylinder.arrow_forwardA 0.5 m x 2 m flat plate is towed at 5 m/s on a 2-mm-thick layer of SAE-30 oil at 38°C that separates it from a flat surface. The velocity distribution between the plate and the surface is assumed to be lincar. What force is required if the plate and surface are horizontal? 1.4arrow_forwardQ. 6 A 4.5-cm wide space between two plates is filled with SAE 30W lubricating oil at 26.7°C (Hoil = 0.301645 N.S/m2 ). What is the area of a very thin plate which is dragged by a force of 18 N through the oil at velocity of 16 m/min if the plate is 1.5 cm away from one of the fixed surfaces?arrow_forward
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