An incompressible liquid with a density of 900 kg/m3 and negligible viscosity flows steadily through a horizontal pipe of constant diameter. In a porous section of length L = 2 m, liquid is removed at a variable rate along the length so that the uniform axial velocity in the pipe is u(x) = Ue−x/L, where U = 20 m/s. Develop expressions for and plot the acceleration of a fluid particle along the centerline of the porous section and the pressure gradient along the centerline. Evaluate the outlet pressure if the pressure at the inlet to the porous section is 50 kPa gage.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Additional Engineering Textbook Solutions
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
Fundamentals Of Thermodynamics
DeGarmo's Materials and Processes in Manufacturing
Introduction to Heat Transfer
Manufacturing Engineering & Technology
- 2. Consider a flow with the velocity profile given by the equation below. The fluid surface is located at y = 0. Here, U∞ is called the freestream velocity and 8 is called the boundary layer thickness. Calculate the boundary layer thickness at a point where the shear stress is 36 mPa if the freestream velocity is 40 m/s and the fluid's dynamic viscosity 1.81.105 Pa.s. U.. ( 2 (²) - (²) ²) u(y) = U∞oarrow_forward9- It flows (10 cm³) of olive oil during a capillary tube (2 cm in length and (0.04 mm in diameter) If the height of the olive oil in the capillary tube (2.5 cm), calculate the time of the olive oil flow into the capillary tube, if you know that the viscosity of the oil ( n oil = 0.18 N .sec/m? ) density of oil (0.918 )? cm VX II >arrow_forwardA long wire of length L to be coated moves at a velocity V0 through a long cylindrical diefilled with an incompressible fluid (density ρ and kinematic viscosity μ). Using cylindricalco-ordinates (r-z) and assuming that pressure is uniform (i.e. dp/dz = 0 and dp/dr = 0).Assume that the flow is steady, laminar and fully developed (neglect any end effects). Clearly4 show all steps, starting from the Navier-Stokes equations, simplifying them, specify properboundary conditions.(a) Find velocity vz as a function of radius inside the die. Use continuity, and momentumequations and clearly show which terms vanish (and why).(b) Also find the force F required to pull the wire in terms of the given known parameterssuch as V0, L, μ, R1, R2 etc.arrow_forward
- m. A piston having a diameter 0.15 m and a length of 0.25 m as shown in figure (1.2) slides downward with a velocity (V) through a vertical pipe. The downward motion is resisted by an oil film between the piston and the pipe wall. The film thickness is 5*10° m, and the cylinder weighs 2.22 N. Estimate V if the oil viscosity is 0.016 N.s/m². Assume the velocity distribution in the gap is linear. 2. Figure (1.1) W D Figure (1.2) Scanned with CamScannerarrow_forwardThe velocity of the mercury at T_∞=250 o C is U_∞=0.033m/sec, and it flows over the pipe bundle of D= 1.25 cm diameter and L=1.2m length. The ratio of the vertical and diagonal spacing distances for the pipes in the shifted plate arrangement is ST /D=SD /D= 1.405. It consists of a matrix with the number of pipe rows in the horizontal direction NL=60 and the number of pipe rows in the vertical direction NT=30. Pipe wall (surface) temperatures are kept at a uniform temperature of T_w=160 o C. Accordingly, find the average heat transfer coefficient, the total heat transfer coefficient from the mercury to the pipe bundle. (Variables: ST /D=SD /D= 0.75-1.975, U=0.02-0.07m/s, L=0.5-1.4m)arrow_forwardConsider flow of an incompressible fluid of density ρ and viscosity µ through a long, horizontal round pipe of diameter D. V is the average speed remains constant down the pipe. For a very long pipe, the flow eventually becomes fully developed, which means that the velocity profile also remains uniform down the pipe. Because of frictional forces between the fluid and the pipe wall, there exists a shear stress τw on the inside pipe wall. We assume some constant average roughness height, along the inside wall of the pipe. In fact, the only parameter that is not constant down the length of pipe is the pressure, which must decrease (linearly) down the pipe in order to “push” the fluid through the pipe to overcome friction. Develop a nondimensional relationship between shear stress τw and the other parameters in the problem.arrow_forward
- (a) A Newtonian fluid having a specific gravity of 0.95 and a kinematic viscosity of 4.2 x 10“m/s flows past a fixed surface as shown in Figure la. The “no-slip" condition suggests that the velocity of the fluid at the fixed surface is zero. The fluid velocity profile away from the fixed surface is given by the equation below: и Зу 1, U 28 2 where U is the constant maximum velocity and its value is 2 m/s. Given that the shear stress developed at the fixed surface is 0.12 N/m², determine the thickness of the fluid, d. Figure la: Fluid velocity profile (b) The clutch system shown in Figure 1b is used to transmit torque through a 3 mm thick clutch oil film with µ = 0.38 Ns/m² between two identical 25 cm diameter disks. When the driving shaft rotates at a speed of 100 rpm, the driven shaft is observed to be stationary. Assuming a linear velocity profile for the oil film, determine the transmitted torque and the power required. Driving shaft Driven shaft 25 cm 3 mm Clutch oil Figure 1b:…arrow_forwardOil flows between two very long parallel plates, separated from H, with width b. The bottom plate moves with speed U and is isolated. The upper plate is at rest and receives heat from the environment at a rate equal to qs". Consider laminar flow, thermally developed. Due to the high viscosity of the fluid, viscous dissipation is relevant U isolada 1 - Estimate the velocity profile considering the null pressure gradient and determine the average speed. 2. Determine dissipation per volume unit. 3. Set mixing temperature and determine the mixing temperature variation over the plates.arrow_forwardHelp me plsarrow_forward
- A piston having a diameter of 9in. and a length of 995in. slides downward with a velocity V through a vertical pipe. The downward motion is resisted by an oil film between the piston and the pipe wall. The film thickness is 90000 in., and the cylinder weighs 7836lb. Estimate V if the oil kinematic viscosity is 7800 ft'/s and its density 432 slugs/ft.Assume the velocity distribution in the gap is linear.arrow_forward1. A fluid is flowing steadily through a vertical tube of length L and radius R. It has constant density and viscosity. Pressure at the tube entrance and exit are Po and PL .Take appropriate assumption and coordinate system and write the differential equations to solve the flow field. Also state the boundary conditions that are applicable here. Po P.arrow_forwardA Newtonian fluid flows in the annular space created by a concentric pipe and rod moving to the right at a constant velocity V (this could be the configuration of a wire coating process). The flow is the result of the shear stress created by the moving rod. The flow is steady and incompressible. Assume u, is only a function of r, both u, and ue (as well as their derivatives) are zero, the pipe is horizontal, and the pressure gradient in the z direction is constant. Derive an expression for the velocity profile uz as a function of r. Note: R, is the inside radius of the outer pipe and R; is the radius of the moving rod. R. R; Varrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY