Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 10, Problem 103P
To determine
The location where the boundary layer begins the transition process towards the turbulence.
The location where the boundary layer becomes fully turbulent.
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Problem 5:
10-103 Air at 30°C flows at a uniform speed of 30.0 m/s along a smooth flat plate. Calculate the approximate x-location along
the plate where the boundary layer begins the transition process toward turbulence. At approximately what x-location along the
plate is the boundary layer likely to be fully turbulent? Answers: 5 to 6 cm, 1 to 2 m
An approximation for the boundary-layer shape in
is the formula
u(y) - U sin
0 sys d
where U is the stream velocity far from the wall and d is the
boundary layer thickness, as in Fig.
If the fluid is
helium at 20°C and 1 atm, and if U = 10.8 m/s and 8= 3 cm,
use the formula to (a) estimate the wall shear stress Tw in
Pa, and (b) find the position in the boundary layer where t
is one-half of Tw.
-- y = 6
u(y)
A flow of air at 37m/s and at 1.6m from the leading edge. The transition Reynolds number is 3 x 10^5. If the boundary layer is laminar at this point If the boundary layer is turbulent at this point What is the boundary layer thickness in metres? Assuming that the air density is 1.226 kg/m3 and dynamic viscosity is 1.79 x 10-5 kg/ms
Chapter 10 Solutions
Fluid Mechanics: Fundamentals and Applications
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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- Air at 1000C flows at an inlet velocity of 2 m/s between two parallel flat plates spaced 1 cm apart. Estimate the distance from the entrance to the point where the boundary layers meet.arrow_forwardFor flow over a smooth plate, what approximately is the maximum length of the boundary layer if V_o = 9.0 m/s in the irrational uniform flow and the fluid is air? Water?arrow_forwardQ1- Air at 27°C and 1 atm flows over a flat plate at a speed of 2 m/s. Calculate the boundary- layer thickness at distances of 20 cm and 40 cm from the leading edge of the plate. The viscosity of air at 27°C is 1.85×105 kg/m. s. density of air 1.177kg/m³arrow_forward
- Experimental studies have shown that the rate of the decay of kinetic energy for homogeneous isotropic turbulence (HIT) is k~t¯", with 1.1arrow_forwardQI/ If the velocity profile of the boundary layer is :O find the thickness of boundary layer, the shear stress at trailing edge and the drag force on one side of plate 2 m long, if it is immersed in water flowing with velocity of 0.4 m/s (p 998 D = 1.007*10-6 m2/s %3Darrow_forwardQ/ Prove that the drag force expression for the boundary layer with the velocity profile -Sin ) is given by the: EoD= 0,6588U?L %3Darrow_forwardWhich one of the following is not a flow region where the boundary layer approximation may be appropriate? (a) Jet (b) Inviscid region (c) Wake (d ) Mixing layer (e) Thin region near a solid wallarrow_forwardOn a hot day (T = 30°C), a truck moves along the highway at 29.1 m/s. The flat side of the truck is treated as a simple, smooth flat–plate boundary layer, to first approximation. Estimate the x-location along the plate where the boundary layer begins to transition to turbulence. How far downstream from the beginning of the plate do you expect the boundary layer to become fully turbulent? Give both answers to one significant digit.arrow_forwardAssume velocity distribution in laminar boundary layer over flat plate to follow the law. u/U= sin(ny/28) obtain expressions 8/0 and 8/x. 25arrow_forwardA 20 °C water flows to 50cmx60cm flat plate with velocity of 3m/s . The flat plate surface temperature is maintained at 40 °C. The air flows parallel to the 50cm side of the plate. If the kinematic viscosity of water is 78x10-8 m2/s, at what length the flow become turbulent?arrow_forward(b) In two-dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = 8. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. Table 2: Equation of Velocity Profile Equation u/U = 3(y/S)/2 – (y/8)³/2arrow_forwardLocal boundary layer effects, such as shear stress and heattransfer, are best correlated with local variables, rather usingdistance x from the leading edge. The momentum thicknessθ is often used as a length scale. Use the analysis of turbulentflat-plate flow to write local wall shear stress τw in terms ofdimensionless θ and compare with the formula recommendedby Schlichting: Cf ≈ 0.033 Reθ -0.268.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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