FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
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Chapter 10, Problem 83P
On a hot day
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If a missile takes off vertically from sea level and leavesthe atmosphere, it has zero drag when it starts and zerodrag when it finishes. It follows that the drag must be amaximum somewhere in between. To simplify the analysis,assume a constant drag coefficient, CD, and constant verticalacceleration, a. Let the density variation be modeled by thetroposphere relation. Find an expression for thealtitude z* where the drag is a maximum. Comment onyour result.
Some engineers want a good estimate of drag and boundary-layerthickness at the trailing edge of a miniature wing. The chord and span ofthe wing are 6 mm and 30 mm, respectively and a typical flight speed is5 m/s in air (kinematic viscosity = 15 × 10−6 m2/s; density = 1.2kg/m3). An engineer may decide to make a superseding model withchord and span of 150 mm and 750 mm, respectively. Measurements onthe model in a water channel flowing at 0.5 m/s (kinematic viscosity = 1× 10−6 m2/s, density = 1000 kg/m3) give a drag of 0.19 N and aboundary-layer thickness of 3 mm. Estimate the corresponding values forthe prototype
Chapter 10 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
Ch. 10 - Discuss how nondimensalizsionalization of the...Ch. 10 - Prob. 2CPCh. 10 - Expalain the difference between an “exact”...Ch. 10 - Prob. 4CPCh. 10 - Prob. 5CPCh. 10 - Prob. 6CPCh. 10 - Prob. 7CPCh. 10 - A box fan sits on the floor of a very large room...Ch. 10 - Prob. 9PCh. 10 - Prob. 10P
Ch. 10 - Prob. 11PCh. 10 - In Example 9-18 we solved the Navier-Stekes...Ch. 10 - Prob. 13PCh. 10 - A flow field is simulated by a computational fluid...Ch. 10 - In Chap. 9(Example 9-15), we generated an “exact”...Ch. 10 - Prob. 16CPCh. 10 - Prob. 17CPCh. 10 - A person drops 3 aluminum balls of diameters 2 mm,...Ch. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 25PCh. 10 - Prob. 26PCh. 10 - Prob. 27PCh. 10 - Consider again the slipper-pad bearing of Prob....Ch. 10 - Consider again the slipper the slipper-pad bearing...Ch. 10 - Prob. 30PCh. 10 - Prob. 31PCh. 10 - Prob. 32PCh. 10 - Prob. 33PCh. 10 - Prob. 34EPCh. 10 - Discuss what happens when oil temperature...Ch. 10 - Prob. 36PCh. 10 - Prob. 38PCh. 10 - Prob. 39CPCh. 10 - Prob. 40CPCh. 10 - Prob. 41PCh. 10 - Prob. 42PCh. 10 - Prob. 43PCh. 10 - Prob. 44PCh. 10 - Prob. 45PCh. 10 - Prob. 46PCh. 10 - Prob. 47PCh. 10 - Prob. 48PCh. 10 -
Ch. 10 - Prob. 50CPCh. 10 - Consider the flow field produced by a hair dayer...Ch. 10 - In an irrotational region of flow, the velocity...Ch. 10 -
Ch. 10 - Prob. 54CPCh. 10 - Prob. 55PCh. 10 - Prob. 56PCh. 10 - Consider the following steady, two-dimensional,...Ch. 10 - Prob. 58PCh. 10 - Consider the following steady, two-dimensional,...Ch. 10 - Prob. 60PCh. 10 - Consider a steady, two-dimensional,...Ch. 10 -
Ch. 10 - Prob. 63PCh. 10 - Prob. 64PCh. 10 - Prob. 65PCh. 10 - In an irrotational region of flow, we wtite the...Ch. 10 - Prob. 67PCh. 10 - Prob. 68PCh. 10 - Water at atmospheric pressure and temperature...Ch. 10 - The stream function for steady, incompressible,...Ch. 10 -
Ch. 10 - We usually think of boundary layers as occurring...Ch. 10 - Prob. 73CPCh. 10 - Prob. 74CPCh. 10 - Prob. 75CPCh. 10 - Prob. 76CPCh. 10 - Prob. 77CPCh. 10 - Prob. 78CPCh. 10 - Prob. 79CPCh. 10 - Prob. 80CPCh. 10 - Prob. 81CPCh. 10 -
Ch. 10 - On a hot day (T=30C) , a truck moves along the...Ch. 10 - A boat moves through water (T=40F) .18.0 mi/h. A...Ch. 10 - Air flows parallel to a speed limit sign along the...Ch. 10 - Air flows through the test section of a small wind...Ch. 10 - Prob. 87EPCh. 10 - Consider the Blasius solution for a laminar flat...Ch. 10 - Prob. 89PCh. 10 - A laminar flow wind tunnel has a test is 30cm in...Ch. 10 - Repeat the calculation of Prob. 10-90, except for...Ch. 10 - Prob. 92PCh. 10 - Prob. 93EPCh. 10 - Prob. 94EPCh. 10 - In order to avoid boundary laver interference,...Ch. 10 - The stramwise velocity component of steady,...Ch. 10 - For the linear approximation of Prob. 10-97, use...Ch. 10 - Prob. 99PCh. 10 - One dimension of a rectangular fiat place is twice...Ch. 10 - Prob. 101PCh. 10 - Prob. 102PCh. 10 - Prob. 103PCh. 10 - Static pressure P is measured at two locations...Ch. 10 - Prob. 105PCh. 10 - For each statement, choose whether the statement...Ch. 10 - Prob. 107PCh. 10 - Calculate the nine components of the viscous...Ch. 10 - In this chapter, we discuss the line vortex (Fig....Ch. 10 - Calculate the nine components of the viscous...Ch. 10 - Prob. 111PCh. 10 - The streamwise velocity component of a steady...Ch. 10 - For the sine wave approximation of Prob. 10-112,...Ch. 10 - Prob. 115PCh. 10 - Suppose the vertical pipe of prob. 10-115 is now...Ch. 10 - Which choice is not a scaling parameter used to o...Ch. 10 - Prob. 118PCh. 10 - Which dimensionless parameter does not appear m...Ch. 10 - Prob. 120PCh. 10 - Prob. 121PCh. 10 - Prob. 122PCh. 10 - Prob. 123PCh. 10 - Prob. 124PCh. 10 - Prob. 125PCh. 10 - Prob. 126PCh. 10 - Prob. 127PCh. 10 - Prob. 128PCh. 10 - Prob. 129PCh. 10 - Prob. 130PCh. 10 - Prob. 131PCh. 10 - Prob. 132PCh. 10 - Prob. 133PCh. 10 - Prob. 134PCh. 10 - Prob. 135PCh. 10 - Prob. 136PCh. 10 - Prob. 137PCh. 10 - Prob. 138P
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- e. b. C. d. a. EME3026 Question 2 A dimensionless velocity profile, u* = u/U = Co + C₁-C₂y, where, y = y/8, is proposed to approximate the laminar boundary layer solution for flow around a corner. The outer flow velocity can be expressed as, U = C²x, where, C, is constant. Boundary layer has the thickness of, 8, where, Co. C₁, and C₂, are the constants to be determined in order to match the boundary conditions in the boundary layer, including the no slip condition, match the outer flow velocity and zero shear stress at the edge of the boundary layer. Apart from that, an additional boundary condition is proposed. a²u dyz y=0 Given the fluid kinematic viscosity, v = 1.46 x 10-5 m²/s and the constant, C² = 0.09 s-¹. Validate the proposed additional boundary condition. FLUID DYNAMICS U (dU Find the velocity profile, u", by evaluating the constant, Co, C₁, and C₂. = --- Determine the displacement thickness and momentum thickness in term of boundary layer thickness. Show that the general…arrow_forwardQuestion 3 The aerodynamic derivative X, may be determined from the following expression: X -pU SCD %3D where p is the air density, S is the wing area, U is the airspeed, and Cp is the drag coefficient. Consider an aircraft of weight 68 kN and wing area 43 m?, flying straight and level under international standard atmosphere (ISA) conditions, where p 1.018 kg/m, at an airspeed of 155 m/s. The aircraft %3D has a drag polar Cp = 0.011 + where Ci is the lift coefficient. Calculate the value of X, at this flight condition. Give your answer in units of Ns/m.arrow_forwardQuestion A3 a) With the help of sketches briefly describe the main differences between laminar and turbulent boundary layers in relation to friction drag and flow separation. A tug boat is pulling a log raft (Figure QA3) on the surface of a lake at a constant speed of Uboat = 5m/s. The log raft can be modelled as a flat plate (L=20m and W = 5.0m). u ug U boat 8 U Tug Boat rope boat Air Water L -X Log Raft Figure QA3 Assume the boundary layer forming on both sides (air side and water side) of the log raft is two-dimensional and laminar with a second order velocity distribution: W b) By using the Momentum Integral Equation find an expression for the wall shear stress in terms of Reynolds number and then estimate the tensile stress acting on the rope assuming the rope has a circular cross section with a diameter of 15 mm) and the power required to pull it. c) What would be the tensile stress on the rope if we assume the boundary layers on the log raft were turbulent? You may assume:…arrow_forward
- Mention the name of a technique which can be used to control the boundary layerarrow_forwardReference 12 contains inviscid theory calculations for the upper and lower surface velocity distributions V(x) over an airfoil, where x is the chordwise coordinate. A typical re- sult for small angle of attack is as follows: xlc VIU„(upper) VIU„(lower) 0.0 0.0 0.0 0.025 0.97 0.82 0.05 1.23 0.98 0.1 1.28 1.05 1.13 0.2 1.29 0.3 1.29 1.16 0.4 1.24 1.16 0.6 1.14 1.08 0.8 0.99 0.95 1.0 0.82 0.82 Use these data, plus Bernoulli's equation, to estimate (a) the lift coefficient and (b) the angle of attack if the airfoil is symmetric.arrow_forwardI need the answer as soon as possiblearrow_forward
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