Problem C. For laminar flow in a circular pipe, show that (a) average velocity equals Vmax/2;...
In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway between the wall surface and the centerline) is measured to be 91 m/s. Determine the velocity at the center of the pipe. The velocity at the center of the pipe m/s
Problem 2 Find the velocity profile for steady, fully-developed, laminar flow in a circular pipe. Integrate this velocity profile to find the mass flowrate through a pipe of length L for a given pressure drop Ap.
Fluid Mechanics #1 Laminar Flow in Pipes The axial velocity in a pipe of radius R is given by, . Find the value of r (as a fraction of R) that maximizes u(r). How does this value of velocity compare with Vc? Compute the wall shear stress, du or Perform a control volume analysis on a pipe section of length e. Relate the pressure drop across the pipe section to the shear stress. Substitute the relation above for tw to...
3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is parabolic: u(0) -4J Figure 2 where u(r) is the velocity at any position r, ß is a constant,-11s the viscosity of water, and r is the radial distance from the pipe centerline. (a) Develop an equation for u(r) assuming a parabolic velocity profile and using the known velocities at the walls u(ro)-0 and the center u(0) (Just use symbols). (b) Develop an equation for shear...
The laminar flow of a permanent incompressible Newtonian fluid in a long cylindrical pipe with a diameter D in vertical position is considered. Gravitational effects are taken into account, flow is carried out with a constant pressure gradient and gravity effect in the z- direction. a. Express the problem on the figure, write the given and accepted. b. Find the velocity profile in the fluid. c. Develop the relations that express the volumetric flow and shear stress in the pipe...
2. (20 marks) The fully-developed, laminar fluid flow through a circular pipe is considered to be one dimensional with a velocity profile given by u(r) = Umax(1 - 52/R2), where R is the radius of the pipe, r is the radial distance from the center of the pipe, and Umax is the maximum flow velocity at the center of the pipe. a) Derive a relation for the drag force applied by the fluid on a section of the pipe of...
5.16. Water is flowing in a 3-cm-diameter pipe at an average velocity of Uav 2 m/s. Assuming water density of ρ-1000 kg/m 3 and viscosity μ-10-3 N s'm2, calculate the velocity at the center of the pipe, the shear τ at the wall, and the Reynolds number. Assuming laminar flow, calculate friction coefficient C and pressure drop dp/dx.
Problem 1: Consider laminar pipe flow having a thermal entrance region and constant wall temperature. Suppose the average Nusselt number is given by the correlation: Nul 3.66+0.0668G 1+0.04Ga 2/3 1 Derive an expression for the local Nusselt number Nu, Problem 1: Consider laminar pipe flow having a thermal entrance region and constant wall temperature. Suppose the average Nusselt number is given by the correlation: Nul 3.66+0.0668G 1+0.04Ga 2/3 1 Derive an expression for the local Nusselt number Nu,
3 PL 23.5 Laminar slit flow with a moving wall ("plane Couette flow"). Extend Problem 23.4 by allow- ing the wall at x B to move in the positive z direction at a steady speed 0 Obtain (a) the shear-stress distribution, and (b) the velocity distribution. 12 Lipuli on Draw carefully labeled sketches of these functions. Answers: (a) „(v) = (*7*2)=- (b) v.Cx) = (*72)P" [1-(0))+ (1+ }) - )B2 ( (b) v(x) = — 1 ... thin it may...
Please explain every thing. Please write in the paper and then take a photo. 1.2. An incompresible fuid fows in a pipe of radius R. At the inlet, sec- tion 1, the velocity is uniform over the tion 2, where the flow is laminar and fully developed, the velocity varies with adius according to the relation V=Vmax (1-R2 (a) Demonstrate that V/Vmax t iu is the average wall shearing stress retarding the flow between see- and 2, fiad the pressure...