Answered: Using Buckingham Pi theorem to find the…

Using Buckingham Pi theorem to find the coefficients of equation: Pi=[density, running speed, diameter, viscosity]=[ρa1, Nb1, Dc1, μ]

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

(6) A dimensionless group called the Reynolds number is defined for a flow in a pipe or tube DV p NRe %3D uV/D Where V is the average velocity in the pipe, p is the fluid density, u is the fluid viscosity, D is the tube diameter. The second form of the group indicates that it is a ratio of the convective (turbulent) momentum flux to the molecular (viscous) momentum flux, or the ratio of inertial forces (which are destabilizing) to viscous forces (which are stabilizing). When viscous forces dominate over inertial forces, the flow is laminar and fluid elements flow in smooth, straight streamlines, whereas when inertial forces dominate, the flow is unstable and the flow pattern break up into random fluctuating eddies It is found that laminar flow in a pipe occurs as long as the value of Reynolds number is less than 2000. Calculate the maximum velocity and the corresponding flow rate (in cm'/s) at which lamina: tlow of water is possible in tubes with the following diameters: 0.64, 1.27,…
Please try to solve in 1 hour
Which of the following dimensionless parameters is the correct arrangement of the given parameters? (select all that O a. Pi = (Dp)/(Rho*V) Dp: Pressure change Rho: Density V: Velocity O b. Pi = (V*L*(Rho))/(nu) V: Velocity L: length Rho: Density nu: Dynamic viscosity O. Pi = Q/((A^1.5)*w) Q: Volumetric discharge rate A: Area w: Angular velocity O d. Pi = (a)(t^2)/(L) L: length a: acceleration t time
(Dimensional Analysis) If the velocity V in a fluid flow depends on a dimension 1, the fluid density p, and the viscosity µ, show that this implies that the Reynolds number Vlp/µ is constant.
P2, µ2 2h P1 Po ρ1, μι L Figure 3: Two layer flow for (b) (b) Consider two immiscible (do not mix) fluid layers with different densities and viscosities which glide smoothly between two parallel horizontal walls, as shown in figure 3. Let pı and p2 be the densities and µ1 and µ2 be the viscosities of the two fluids, respectively. The flow is the result of an imposed constant pressure gradient, 2, similar to that of the Poiseuille flow. Assume a steady, incompressible, parallel viscous flow with p1 > P2 and µi > µ2- (i) Using the Navier-Stokes equations find the velocity profiles of both fluids. (ii) Ensure the fluid obeys the following conditions: The shear stress is continuous at the interface between the two fluids. • The velocity profile is continuous at the interface between the two fluids. No-slip boundary at the walls. (iii) Sketch the velocity profile. (iv) Determine where the maximum velocity occurs and explain why. (Hint: think about the respective viscosities and densities).…
A thin layer of spherical particles rests on the bottom of a horizontal tube as shown in the figure below. When an incompressible fluid flows through the tube, it is observed that at some critical velocity the particles will rise and be transported along the tube. A model is to be used to determine this critical velocity. Assume the critical velocity, V, to be a function of the pipe diameter, D, particle diameter, d, the fluid density, p, and viscosity, μ, the density of the particles, Pp, and the acceleration of gravity, g. For a length scale of Dm/D=1/2 and a fluid density scale of Pm/p=1/0.9, what will be the critical velocity scale V/V (assuming all similarity requirements are satisfied)? Vm/V= i
X2 = 5x1 + 5x2 - 7x3
Wind tunnel test section km/h Model FD Moving belt Drag balance The aerodynamic drag of a new Volvo FH truck is to be predicted at a speed of 85 km/h at an air temperature of 25°C (p=1.184 kg/m³, u=1.849x10-5kg/m-s). Volvo engineers build a 1/2 scale model of the FH to test in a wind tunnel. The temperature of the wind tunnel is also 25°C. The drag force is measured with a drag balance, and the moving belt is used to simulate the moving ground. Determine how fast the engineers should run the wind tunnel to achieve similarity between the model and the prototype.
For a venturi meter given below, the volumetric flow rate is defined in terms of the geometrical parameters, the density of working fluid (p), and density of the manometer liquid (pm) as 4. Q = f(D, D2, A2, g, h, Pmv Pr) %3D Write down the balance equations and show your work to end up with an expression for the volumetric flow rate in terms of the variables defined above.
Check the following equation for dimensional homogeneity: mv = [₁² ( (Fcose) dt where m is mass, v is velocity, F is force, 0 is an angle, and t is time. Check that each term in the equation has the following dimensions: [MªLºTc] where you are to choose the coefficients a, b, c. Answers: a = i b= i C = i
A race car increases its speed from 80 mi/h to 160 mi/h in a distance of 100m. Find the magnitude of its acceleration and the time it takes the car to cover the 100- m distance. [1 mi = 1609 m] %3D
Measurements at a certain point of a pipe have been done where the following parameters were recorded: Fluid of density = 887 kg/m3, Fluid velocity = 4 m/s, Pressure= 11.3 KN/m2 If the total energy per unit weight at this point = 32 m, then the potential energy is: