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Chapter 4 Solutions
FLUID MECHANICS >C<
- A power plant discharges cooling water through the manifoldin Fig. which is 55 cm in diameter and 8 m highand is perforated with 25,000 holes 1 cm in diameter. Does this manifold simulate a line source? If so, what is theequivalent source strength m?arrow_forwardWater at 20°C flows past a 1-m-diameter circular cylinder.The upstream centerline pressure is 128,500 Pa. If the lowestpressure on the cylinder surface is exactly the vaporpressure, estimate, by potential theory, the stream velocity.arrow_forwardAssume 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. Prove that the flow field specified is not incompressible;i.e., it is a compressible flow as stated without proof .arrow_forward
- For the pitot-static pressure arrangement of Fig.,the manometer fluid is (colored) water at 20°C. Estimate(a) the centerline velocity, (b) the pipe volume flow, and(c) the (smooth) wall shear stress.arrow_forwardAir flows through a 6-cm-diameter smooth pipe that has a2-m-long perforated section containing 500 holes (diameter1 mm), as in Fig. . Pressure outside the pipe issea-level standard air. If p1 = 105 kPa and Q1 = 110 m3/h,estimate p2 and Q2, assuming that the holes are approximatedby thin-plate orifices. (Hint: A momentum controlvolume may be very useful.)arrow_forwardThe Rankine body of revolution in Fig. is 60 cm longand 30 cm in diameter. When it is immersed in the low-pressurewater tunnel as shown, cavitation may appear atpoint A. Compute the stream velocity U, neglecting surfacewave formation, for which cavitation occurs.arrow_forward
- A wedge split a sheet of 20°C water in the air. Both wedge and sheet are 1 m long into the paper. The wedge angle is 60 degrees, the sheet thickness is Y cm and the sheet velocity is Y m/s. What is the required force to hold the wedge stationary? Assume Y is 4 (Hint, you can assume a uniform velocity distributionarrow_forwardQ2 Fluid mechanics With respect to the stream function, develop the superposition for two cases: - Uniform + Dipole - Uniform + Dipole (a->0)arrow_forward1. For a certain incompressible two-dimensional flow, the stream function, ψ(x, y) is prescribed. Is the continuity equation satisfied? 2. If u = −Ae−ky cos kx and v = −Ae−ky sin kx, find the stream function. Is this flow rotational, or irrotational?arrow_forward
- For the flow field given in Cartesian coordinates by u = 0, v = x2z, w = z3: (a) Is the flow compressible? (b) What is the y-component of the acceleration following a fluid particle?arrow_forwardConsider a uniform stream of magnitude V inclined at angle ?. Assuming incompressible planar irrotational flow, find the velocity potential function and the stream function. Show all your work.arrow_forwardAssume 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. Consider a venturi with a small hole drilled in the side of the throat. Thishole is connected via a tube to a closed reservoir. The purpose of theventuri is to create a vacuum in the reservoir when the venturi is placed inan airstream. (The vacuum is defined as the pressure difference below theoutside ambient pressure.) The venturi has a throat-to-inlet area ratio of0.85. Calculate the maximum vacuum obtainable in the reservoir when theventuri is placed in an airstream of 90 m/s at standard sea level conditions.arrow_forward
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