Poiseuille flow describes laminar flow in a circular pipe. The velocity distribution in such flow has...

Poiseuille flow describes laminar flow in a circular pipe. The velocity distribution in such flow has a parabolic form. Prove that the mean velocity is equal to one-half of the maximum velocity in this type of flow. Be sure to show all of your work. (Hint: the analysis is similar to that done for laminar flow between parallel plates)

Expert Solution

samet mamat answered 2 years ago

The velocity profile for a steady laminar flow in a circular pipe of radius R is...

The velocity profile for a steady laminar flow in a circular pipe of radius R is given by u=u0(1−r2R2) . If the fluid density varies with radial distance r from the centerline as ρ=ρ0(1+rR)14 , where ρ0 is the fluid density at the pipe center, obtain and choose the correct relation for the bulk fluid density in the tube.

The velocity profile for a steady laminar flow in a circular pipe of radius R given...

The velocity profile for a steady laminar flow in a circular pipe of radius R given be u=u0( 1- r^2/R^2). if the fluid density varies with radial distance r from the centerline as p=p0 ( 1+ r/R)^1/4 where p0 is the fluid density at the pipe center, obtain a relation for the bulk fluid density in the tube.

For laminar flow in a circular pipe of diameter , at what distance from the centerline...

For laminar flow in a circular pipe of diameter , at what distance from the centerline is the actual velocity equal to the average velocity? Answer as a decimal version of the fraction of . For instance, for enter 0.25.

Fully developed (both hydrodynamic and thermal) laminar flow is pushed through a thin-walled circular pipe of...

Fully developed (both hydrodynamic and thermal) laminar flow is pushed through a thin-walled circular pipe of diameter 13 mm. The fluid flows through the pipe at a velocity of 0.1 m/sec, has a density of 1000 kg/m^3, a dynamic viscosity of 855 x 10^-6 Pa-sec, a specific heat of 4000 J/kg-K, a Prandtl number of 8, and a thermal conductivity of 0.613 W/(m-K). The outside of the pipe is subjected to uniform cross flow where the free-stream velocity is 5...

You are studying the laminar flow of water in a pipe at 20˚C. The pipe is...

You are studying the laminar flow of water in a pipe at 20˚C. The pipe is 2 cm in diameter, and the pressure gradient driving the flow is 0.8 Pa/m. Find the x-sectional average velocity (Poiseuille’s Law) and the maximum velocity achieved at the centerline of the pipe (use the equation for Umax presented in the alternative derivation of Poiseuille’s Law). How many times greater is the maximum velocity compared to the average velocity? Is this ū/umax ratio constant or...

6. An increase in roughness of a pipe with laminar flow would increase the pressure drop...

6. An increase in roughness of a pipe with laminar flow would increase the pressure drop of the pipe. Assume the velocity is the same for the smooth pipe and the rough pipe. a. True b. False

calculate the maximum velocity and the correspondingbvolumetric flow rate (in/cm^3/s) at which laminar flow of air...

calculate the maximum velocity and the correspondingbvolumetric flow rate (in/cm^3/s) at which laminar flow of air and water is possible in pipes with the following diameter D=.25,.5,1.0,2.0,4.0,6.0, and 10.0in

(a) For a 1.25-in.-diameter pipe, what is the maximum volumetric flow rate at which water can be pumped and the flow will remain laminar?

(a) For a 1.25-in.-diameter pipe, what is the maximum volumetric flow rate at which water can be pumped and the flow will remain laminar? Express your result in the dimensions of gallons per minute. (b) What would be the maximum fl ow rate for SAE 30 oil?

Compare the velocity profiles for laminar and turbulent fluid flow. Explain fully one is parabolic and...

Compare the velocity profiles for laminar and turbulent fluid flow. Explain fully one is parabolic and the other more closely resembles a plateau.

Q1. For the given velocity distribution in a pipe: where v(r)=velocity at a distance r...

Q1. For the given velocity distribution in a pipe: where v(r)=velocity at a distance r from the centerline of the pipe, V0=centerline velocity, and R=radius of the pipe. Find the average velocity, energy and momentum correction factors.

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