Fluid Mechanics 6th. Edition by Pijush K. Kundu, Ira M. Cohen, David R Dowling | 9780124071513 | 012405935X | Holooly

Fluid Mechanics

Fluid Mechanics

138 SOLVED PROBLEMS

Question: 5.4

Consider a thin ideal vortex segment of uniform strength G that lies along the z-axis between z1 and z2, and has a sense of rotation that points along the z-axis. Use the BioteSavart law to show that the induced velocity u at the location (R, φ, z) will be u(χ, t) = (Γ=4πR)(cosθ1 – cosθ2)eφ where ...

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Apply (5.17) to the geometry shown with x′ = (0, 0...

Question: 15.5

A convergente−divergent nozzle is operating under off-design conditions, resulting in the presence of a shock wave in the diverging portion. A reservoir containing air at 400 kPa and 800 K supplies the nozzle, whose throat area is 0.2 m². The Mach number upstream of the shock is M1 = 2.44. The area ...

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Figure 15.14 shows the profile of the nozzle, wher...

Question: 15.4

A normal shock wave forms just ahead of a bullet as it travels at 750 m/s through still air at 100 kPa and 295 K. What are the pressure, temperature, and density of the air immediately behind the shock wave? ...

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Ahead of the bullet, the density is:

\rho_1...

Question: 15.8

A uniform flow at atmospheric pressure having M1 = 3.0 is deflected by 20°. What are the Mach number and pressure in the flow after the deflection if it occurs through (a) an oblique shock wave from a compression corner (Figure 15.23 right side panel), (b) an isentropic compression from a curved ...

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For (a) an oblique shock wave must be considered. ...

Question: 15.3

The nozzle of a rocket motor is designed to generate a thrust of 30,000 N when operating at an altitude of 20 km. The pressure and temperature inside the combustion chamber are 1000 kPa and 2500 K. The gas constant of the gas in the jet is R = 280 m²/(s² K), and γ = 1.4. Assuming that the flow in ...

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At an altitude of 20 km, the pressure of the stand...

Question: 15.9

Determine the lift and drag coefficients of an infinitely-thin but mildly-cambered airfoil at zero angle of attack in a horizontal supersonic flow at speed M∞. ...

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Figure 14.13 shows an infinitely thin cambered foi...

Question: 14.5

If the complex potential in the ζ-plane represents uniform horizontal flow past a cylinder with radius a and clockwise circulation Γ (see Figure 7.12a): w(ζ)=U(ζ + a² /ζ) + iΓ/2πln(ζ/a), set |b| = a and use the transformation from Example 14.4, z = ζ + (aeiα)2/ζ, and the Kutta condition to show ...

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The complex velocity in the ζ-plane is:

\fr...

Question: 15.1

Which of the following are compressible flows? a) A weather balloon rises at 5 m/s from sea level to an altitude of more than 15 km. b) Water flows through the nozzle of a water jet cutter and the gage pressure drops from 100 MPa to zero. c) The piston of an internal combustion engine moves at 15 ...

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The essential feature of compressible flow (as def...

Question: 14.4

Into what shape in the z-plane is the circle defined by ζ = |b|e^iθ in the ζ-plane mapped by the transformation z = ζ + b²/ζ when b is a complex number b = |b|e^−iα when α is a positive real constant? ...

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Set

\zeta=|b|e^{i\theta}

in the giv...

Question: 14.3

As a simplified means to explain how a flying aircraft’s weight is transmitted to the ground, consider two-dimensional ideal flow with density ρ and speed U past an ideal vortex of strength Γ a distance H above an infinite flat surface (see Figure 14.11). Integrate the pressure distribution on the ...

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Choose the flat surface at y = 0, and presume the ...

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