(b) Consider fully developed flow of an incompressible Newtonian liquid in an in-finitely long tube of elliptic cross section, under constant pressure gradient .If gravity is neglected, and the boundary condition applies:Uo 0:a?y?, z21,U =show that the velocity u(y, z) can be written as1 Əp a?b?2µ đx a2 + 62y?u(y, z) =a?

(b Given Data u(y,z)=0y2a2+z2b2=1 On neglecting gravity the consistent state navier stokes…

(b) Consider fully developed flow of an incompressible Newtonian liquid in an in- finitely long tube of elliptic cross section, under constant pressure gradient P. If gravity is neglected, and the boundary condition applies: y?, z2 1, U = 0 on a2 |3D 62 show that the velocity u(y, z) can be written as 1 ap a?6? 2µ Əx a2 + 62 y? z2 (1--) u(y, z) = %3D - | a?

(b) Consider fully developed flow of an incompressible Newtonian liquid in an in- finitely long tube of elliptic cross section, under constant pressure gradient P. If gravity is neglected, and the boundary condition applies: y?, z2 1, U = 0 on a2 |3D 62 show that the velocity u(y, z) can be written as 1 ap a?6? 2µ Əx a2 + 62 y? z2 (1--) u(y, z) = %3D - | a?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter7: Forced Convection Inside Tubes And Ducts

Section: Chapter Questions

Problem 7.20P

See similar textbooks

Similar questions

A 1.0 m radius cylindrical industrial tank filled with viscous oil to a level at a height h from its base, must be drained through a tube with a radius of 0.2 m and length L, connected to its base. The speed profile of oil in the drain tube can be described by the equation below. Where v is the oil speed, vmax is a = maximum oil speed, r is the radius, and R is the tube radius. Considering this problem situation, do what is asked in the following items, justifying your answers. a) What is the volume, in liters, of oil removed from the tank after 10 seconds, if the maximum discharge speed does the oil reach 0.35 m/s? Data: π ≈ 22/7; 1 m3 = 1000 L. b) What flow regime does the system operate? Demonstrate. Data: specific mass of oil = 800 kg/m3, specific mass of water = 1000 kg/m3, oil viscosity = 0.056 Pa.s e viscosity of water = 0.001 Pa.s.
Answer completely Show how the Darcy-Weisbach equation can be derived from the Hagen-Poiseuille equation through the introduction of the Reynolds number. What is the friction factor, f, equal to for flow at a laminar condition? What is it equal to in other regimes of flow?
Combination of available data for transition and turbulent flow in smooth as well as rough pipes into the following implicit relation known as the_________________. Group of answer choices a. Bernoulli’s equation b. Continuity equation c. Colebrook’s equation d. Ideal gas equation
Water at 20 ° C fl ows through a 5-in-diameter smooth pipeat a high Reynolds number, for which the velocity profi le isapproximated by u ≈ U o ( y/R ) 1/8 , where U o is the centerlinevelocity, R is the pipe radius, and y is the distance measuredfrom the wall toward the centerline. If the centerlinevelocity is 25 ft/s, estimate the volume fl ow rate in gallonsper minute.
Carbon dioxide is being pumped through a smooth pipe at the rate of 3×10-4 kmol/sec for a distance of 2000 m. Ifthe line is isothermal at 323.15 K and the pressure at the entry point is 750 ×103 Pa and at the exit point is 430×103 Pa, what diameter should the pipe has to ensure that the CO2 will be delivered to the end point with the pressure drop experienced. The viscosity of CO2 at 323.15 K is 1.45×10-5kg/m.s. One trial is sufficient given you tell us how you will proceed to achieve an accurate diameter estimate. Hint: for your initial guess, use D in the range of 0.01-0.02 m.
Consider laminar flow of a Newtonian fluid ofviscosity m between two parallel plates. The flow is onedimensional,and the velocity profile is given as u(y) = 4umax[ y/h - (y/h)2], where y is the vertical coordinate from thebottom surface, h is the distance between the two plates,and umax is the maximum flow velocity that occurs at midplane.Develop a relation for the drag force exerted on bothplates by the fluid in the flow direction per unit area of theplates.
Pressure Drop of Power-Law Fluid in Laminar FlowA power-law fluid having a density of 1041 kg/m3 is flowing through 14.9 m of a tubing with an inside diameter of 0.0524 m at an average velocity of 0.0728 m/s. The rheological or flow properties of the fluid are K′ = 15.23N·sn′/m2 (0.318 lbf·sn′/ft2) and n′ = 0.40. Calculate the pressure drop and friction loss using Eq. (9.1-10) for laminar flow. Check the generalized Reynolds number to make sure that the flow is laminar. Repeat part (a) but use the friction-factor method
Two incompressible fluids (m1=2m2) are flowing at the same mass flow rates in homogenous pipes with the same diameter. What is the ratio of their Reynolds numbers?
Glycerin, with a density of 1260 kg/m3 and an absolute viscosity of 1.5 kg/m.s, flows in a tube with an internal diameter of 5,0 cm, but it is not known whether the regime is laminar or turbulent. Knowing that the length of the hydrodynamic inlet of this flow is 0.2 m, determine the velocity of the oil and the flow regime. (the form is in the side picture)
What are the applications and principles of Laser-Doppler Anemometer to agricultural and biosystems engineering?
If two cylindrical horizontal pipes are geometrically similar and the flows in themdynamically similar, how will the pressure drops in corresponding lengths vary with density andmean velocity of the fluid?
1. Why we use Reynolds number instead of mean velocity as thecriteria to judge the flow state passing through the pipe? 2. Does the ReDL or the ReDU change when the diameter is changed?3. If we replace the pure water with the oil (Newtonian fluids), doesthe lower limit Reynolds number be the same? Why?