Explanation Given information: Line sink m = − 1000 m 2 s , line vortex K = 1600 m 2 s Take sea level air p = 101.350 k p a , ρ = 1.225 k g / m 3 Calculation: we know that for this flow the stream function is, ψ = − k ln r − m θ And we know that, tan θ = | v θ v r | ------equation 1 Using the relation , v θ = ∂ ψ ∂ r , v r = − 1 r ∂ ψ ∂ θ Differentiate stream function with respect to r ∂ ψ ∂ r = − k 1 r Similarly with respect to θ ∂ ψ ∂ θ = − m We get v θ = − k r , v r = m r Put these values in equation 1 tan θ = ( k / r m / r ) = k m = 1600 1000 = 1

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 8, Problem 8.30P

To determine

Angle between any streamline and radial line?

And show that it is independent of both r,θ.

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Chapter 8, Problem 8.29P

Chapter 8, Problem 8.31P

Chapter 8 Solutions

Fluid Mechanics

Ch. 8 - Prob. 8.1P Ch. 8 - The steady plane flow in Fig. P8.2 has the polar...Ch. 8 - P8.3 Using cartesian coordinates, show that each...Ch. 8 - P8.4 Is the function 1/r a legitimate velocity...Ch. 8 - Prob. 8.5P Ch. 8 - An incompressible plane flow has the velocity...Ch. 8 - Prob. 8.7P Ch. 8 - For the velocity distribution u=By,=+Bx , evaluate...Ch. 8 - Prob. 8.9P Ch. 8 - Prob. 8.10P

Ch. 8 - Prob. 8.11P Ch. 8 - Prob. 8.12P Ch. 8 - P8.13 Starting at the stagnation point in Fig....Ch. 8 - P8.14 A tornado may be modeled as the circulating...Ch. 8 - Hurricane Sandy, which hit the New Jersey coast on...Ch. 8 - Prob. 8.16P Ch. 8 - P8.17 Find the position (x, y) on the upper...Ch. 8 - Prob. 8.18P Ch. 8 - Prob. 8.19P Ch. 8 - Plot the streamlines of the flow due to a line...Ch. 8 - P8.21 At point A in Fig. P8.21 is a clockwise line...Ch. 8 - P8.22 Consider inviscid stagnation flow, (see...Ch. 8 - P8.23 Sources of strength m = 10 m2/s are placed...Ch. 8 - P8.24 Line sources of equal strength m = Ua, where...Ch. 8 - Prob. 8.25P Ch. 8 - Prob. 8.26P Ch. 8 - Prob. 8.27P Ch. 8 - Sources of equal strength m are placed at the four...Ch. 8 - Prob. 8.29P Ch. 8 - Prob. 8.30P Ch. 8 - A Rankine half-body is formed as shown in Fig....Ch. 8 - Prob. 8.32P Ch. 8 - P8.33 Sketch the streamlines, especially the body...Ch. 8 - Prob. 8.34P Ch. 8 - Prob. 8.35P Ch. 8 - Prob. 8.36P Ch. 8 - Prob. 8.37P Ch. 8 - Consider potential flow of a uniform stream in the...Ch. 8 - A large Rankine oval, with a = 1 m and h = 1 m, is...Ch. 8 - Prob. 8.40P Ch. 8 - Prob. 8.41P Ch. 8 - Prob. 8.42P Ch. 8 - P8.43 Water at 20°C flows past a 1-rn-diameter...Ch. 8 - Prob. 8.44P Ch. 8 - Prob. 8.45P Ch. 8 - P8.46 A cylinder is formed by bolting two...Ch. 8 - Prob. 8.47P Ch. 8 - Prob. 8.48P Ch. 8 - Prob. 8.49P Ch. 8 - It is desired to simulate flow past a...Ch. 8 - Prob. 8.51P Ch. 8 - P8.52 The Flettner rotor sailboat in Fig. E8.3...Ch. 8 - P8.52 The Flettner rotor sailboat in Fig. E8.3 has...Ch. 8 - Prob. 8.54P Ch. 8 - Prob. 8.55P Ch. 8 - Prob. 8.56P Ch. 8 - Prob. 8.57P Ch. 8 - Prob. 8.58P Ch. 8 - Prob. 8.59P Ch. 8 - Prob. 8.60P Ch. 8 - Prob. 8.61P Ch. 8 - Prob. 8.62P Ch. 8 - The superposition in Prob. P8.62 leads to...Ch. 8 - Consider the polar-coordinate stream function...Ch. 8 - Prob. 8.65P Ch. 8 - Prob. 8.66P Ch. 8 - Prob. 8.67P Ch. 8 - Prob. 8.68P Ch. 8 - Prob. 8.69P Ch. 8 - Prob. 8.70P Ch. 8 - Prob. 8.71P Ch. 8 - Prob. 8.72P Ch. 8 - Prob. 8.73P Ch. 8 - Prob. 8.74P Ch. 8 - Prob. 8.75P Ch. 8 - Prob. 8.76P Ch. 8 - Prob. 8.77P Ch. 8 - Prob. 8.78P Ch. 8 - Prob. 8.79P Ch. 8 - Prob. 8.80P Ch. 8 - Prob. 8.81P Ch. 8 - Prob. 8.82P Ch. 8 - Prob. 8.83P Ch. 8 - Prob. 8.84P Ch. 8 - Prob. 8.85P Ch. 8 - Prob. 8.86P Ch. 8 - Prob. 8.87P Ch. 8 - Prob. 8.88P Ch. 8 - Prob. 8.89P Ch. 8 - NASA is developing a swing-wing airplane called...Ch. 8 - Prob. 8.91P Ch. 8 - Prob. 8.92P Ch. 8 - Prob. 8.93P Ch. 8 - Prob. 8.94P Ch. 8 - Prob. 8.95P Ch. 8 - Prob. 8.96P Ch. 8 - Prob. 8.97P Ch. 8 - Prob. 8.98P Ch. 8 - Prob. 8.99P Ch. 8 - Prob. 8.100P Ch. 8 - Prob. 8.101P Ch. 8 - Prob. 8.102P Ch. 8 - Prob. 8.103P Ch. 8 - Prob. 8.104P Ch. 8 - Prob. 8.105P Ch. 8 - Prob. 8.106P Ch. 8 - Prob. 8.107P Ch. 8 - P8.108 Consider two-dimensional potential flow...Ch. 8 - Prob. 8.109P Ch. 8 - Prob. 8.110P Ch. 8 - Prob. 8.111P Ch. 8 - Prob. 8.112P Ch. 8 - Prob. 8.113P Ch. 8 - Prob. 8.114P Ch. 8 - Prob. 8.115P Ch. 8 - Prob. 8.1WP Ch. 8 - Prob. 8.2WP Ch. 8 - Prob. 8.3WP Ch. 8 - Prob. 8.4WP Ch. 8 - Prob. 8.5WP Ch. 8 - Prob. 8.6WP Ch. 8 - Prob. 8.7WP Ch. 8 - Prob. 8.1CP Ch. 8 - Prob. 8.2CP Ch. 8 - Prob. 8.3CP Ch. 8 - Prob. 8.4CP Ch. 8 - Prob. 8.5CP Ch. 8 - Prob. 8.6CP Ch. 8 - Prob. 8.7CP Ch. 8 - Prob. 8.1DP Ch. 8 - Prob. 8.2DP Ch. 8 - Prob. 8.3DP

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