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.

Expert Solution

samet mamat answered 2 years ago

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.

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)

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.

Consider laminar steady boundary layer at a flat plate. Assume the velocity profile in the boundary...

Consider laminar steady boundary layer at a flat plate. Assume the velocity profile in the boundary layer as parabolic, u(y)=U(2 (y/δ)-(y/δ)^2). 1. Calculate the thickness of the boundary layer, δ(x), as a function of Reynold's number. 2. Calculate the shear stress at the surface, τ, as a function of Reynold's number. Re=ρUx/μ

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...

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.

Steady, laminar flow in an annulus (flow between two stationary concentric cylinders) Obtain an expression for...

Steady, laminar flow in an annulus (flow between two stationary concentric cylinders) Obtain an expression for the developed velocity Distribution and the volumetric flow rate for a laminar, steady, incompressible, fully developed flow in an annulus.

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

Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two ...

Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates (Figure \(3(a))\). The top plate is moving at speed \(V\), and the bottom plate is stationary. The distance between these two plates is \(h .\) The gravity acts in the \(z\) direction so the flow can be considered essentially two dimensional in \(x-y\) plane. Assume there acts an applied pressure gradient in the \(x\) -direction with its gradient given by, \(\partial P...

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