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For the pressure-gradient flow in a circular tube in Sec. 4.10, reanalyze for the case of slip flow at the wall. Use the simple slip condition
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Fluid Mechanics
- 338 B/s O 1: 56% E 3:01 Question: Gasoline is flowing through this 180° pipe bend. The pipe cross-sectional area is 18 in?. Take the pipe weight as 5 Kg. Flow rate is 0.5 liters/s. Pressure at section-1 6 psia, pressure at section-2 is 4 psia. Calculate the anchoring force required to hold this pipe and also show its direction, referenced to proper 2-dimensional a cartesian coordinate system. (2 1arrow_forwardExample: Given: u = xt+2y y = xt² - yt w = 0 What is the acceleration at a point x=1 m, y=2 m, and at a time t=3 s?arrow_forwardFor the flow of gas between two parallel plates of Fig. 1.7,reanalyze for the case of slip fl ow at both walls. Use thesimple slip condition, δu wall = l ( du/dy ) wall , where l isthe mean free path of the fl uid. Sketch the expected velocityprofile and find an expression for the shear stress ateach wall.arrow_forward
- Q.2 An incompressible fluid (kinematic viscosity, 7.4x10-7 m2, 7.4×10 m/sec, specific gravity, 0.44) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary, then fluid attains a linear velocity profile in the gap of 0.5 mm between these plates. The shear stress (in Pascals) on the surface of bottom plate is 2 0.3256 N/m A 0.4256 N/m C 0.5256 N/m2 2 D 0.6256 N/marrow_forwardA constant-thickness film of viscous liquid flows in laminarmotion down a plate inclined at angle θ , as in Fig. P4.36.The velocity profile isu = Cy(2h - y) υ = w = 0Find the constant C in terms of the specifi c weight andviscosity and the angle θ . Find the volume fl ux Q per unitwidth in terms of these parameters.arrow_forwardUnder laminar conditions, the volume flow Q through asmall triangular-section pore of side length b and length Lis a function of viscosity μ , pressure drop per unit length∆p / L , and b . Using the pi theorem, rewrite this relation indimensionless form. How does the volume flow change ifthe pore size b is doubled?arrow_forward
- A capillary viscometer measures the time required for a specified volume υ of liquid to flow through a small-bore glasstube, as in Fig. . This transit time is then correlated withfluid viscosity. For the system shown, (a) derive an approximateformula for the time required, assuming laminar flowwith no entrance and exit losses. (b) If L = 12 cm, l = 2 cm,υ = 8 cm3, and the fluid is water at 20 °C, what capillary diameterD will result in a transit time t of 6 seconds?arrow_forwardIn Prob. it would be difficult to solve for Ω because of itappears in all three of the dimensionless pump coefficients.Suppose that, in Prob. 5.61, Ω is unknown but D = 12 cmand Q = 25 m 3 /h. The fluid is gasoline at 20 ° C. Rescale thecoefficients, , to make a plot ofdimensionless power versus dimensionless rotation speed.Enter this plot to find the maximum rotation speed Ωforwhich the power will not exceed 300 W.arrow_forwardAn incompressible fluid flows in a linear porous medium with the following properties: Lenth = 3000 ft k = 100 md p1 = 2000 psig p2 = 1980 psig height = 25 ft porosity = 20% width = 300 ft viscosity = 2 cP Assume the dimension is slanted, i.e., a dip angle of 5 degrees (downward from p1 location to p2 location), what is the apparent fluid velocity under this new boundary condition?arrow_forward
- Water is flowing at 0.075 cu.m./sec through a glazed porcelain pipe 400m long and 200mm diameter. The pipe roughness is 0.0015mm. Properties of water: Density: 1,000 g/cu.m., viscosity = 0.001 N-m/sec. What is the velocity of water in the pipe? What is the Reynold's number? Steady State flow exists in pipe that undergoes a gradual expansion from a diameter of 6in. Assuming constant density and the inlet flow velocity is 22.4 ft/sec. What is the size of the exit pipe if the exist flow velocity is 12.6 ft/sec?arrow_forwardQ3) In some wind tunnels the test section is perforated to suck out fluid and provide a thin viscous boundary layer. The test section wall in Fig.3 contains 12064 holes of 5 mm diameter. The suction velocity through each hole is Vs = 8 m/s, and the test section entrance velocity is V₁ = 35 m/s. Assume incompressible steady flow of air at 20°C, compute, Vo, V₂ and Vf in m/s. Test section D₁ = 0.8 m Uniform suction D₁= 2.2 m Do = 2.5 m V₂ -L=4 m Fig.3 L Vo-arrow_forwardQ.2 A flow is described by the stream function v = 25xv, The coordinates of the point at which velocity vector has a magnitude of 4 units and makes an angle 150 ° with the X-axis is A x=1.0, y=0.5774 B X=0.5774, Y=1.0 WRONG C X=1, Y=-0.5774 D X=-1, Y=0.5774arrow_forward
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