An excellent approximation for the two-dimensional incompressible laminar boundary layer on the flat surface in Fig, P4.17 is
(a) Assuming a no-slip condition at the wall, find an expression for the velocity component v(x, y) for y ??. (b) Then mid the maximum value of v at the station x = 1 m, for the particular case of airflow, when U = 3 m/s and
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- Air 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_forwardFor the velocity field: u = 3xy, v = -1.5y²+5; for water, ρ = 1000 kg/m³If the pressure at (0,0) is 100 Pa, what is the pressure at (2,0)?arrow_forwardWater at 20 ° C flows down through a vertical, 6-cm diametertube at 300 gal/min, as in Fig. P3.74. The flowthen turns horizontally and exits through a 90 ° radial ductsegment 1 cm thick, as shown. If the radial outflow is uniformand steady, estimate the forces ( F x , F y , F z ) required tosupport this system against fluid momentum changes.arrow_forward
- A flow field is formed by combining a uniform flow field of 10m/s and a vortex withstrength Γ=4pi m2 /s located at the origin. Find the location of the stagnation point and theequation of the dividing streamline. What are the velocity and pressure coefficients at a pointwith (r,theta)=(1,pi/2)?arrow_forwardA 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_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
- Assume 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 throat-to-inlet area ratio of 0.8, mounted on theside of an airplane fuselage. The airplane is in flight at standard sea level.If the static pressure at the throat is 2100 lb/ft2, calculate the velocity ofthe airplane.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_forwardAir at 20°C and 1 atm flow at 20 m/s past the flat platein Fig. . A pitot stagnation tube, placed 2 mm fromthe wall, develops a manometer head h = 16 mm of Meriamred oil, SG = 0.827. Use this information to estimatethe downstream position x of the pitot tube. Assumelaminar flow.arrow_forward
- See the following nozzle, L is 10 cm, Dentrance is 2 cm, Dexit is 0.5 cm. The volume flow rate through the nozzle is 0.227 m3/h. The flow is steady. Estimate the magnitude of the acceleration of a fluid parcel moving down the centerline of the nozzle.arrow_forwardFor the container of Fig. P3.116 use Bernoulli’s equation toderive a formula for the distance X where the free jet leavinghorizontally will strike the fl oor, as a function of h andH . For what ratio h / H will X be maximum? Sketch the threetrajectories for h / H = 0.25, 0.5, and 0.75.arrow_forwardUsing cartesian coordinates, show that each velocity component(u, υ, w) of a potential flow satisfies Laplace’sequation separately.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning