An incompressible fluid oscillates harmonically (V = Vosinwt, where Vis the velocity) with a frequency of 9 rad/s in a 6-in.-diameter pipe. A 1/5 scale model is to be used to determine the pressure difference per unit length, Ap, (at any instant) along the pipe. Assume that Api= f(D, Vo, w, t, u, p) where D is the pipe diameter, w the frequency, t the time, the u fluid viscosity, and p the fluid density. If the same fluid is used in the model and the prototype, at what frequency should the model operate? Wm i rad/s

An incompressible fluid oscillates harmonically (V = Vosinwt, where Vis the velocity) with a frequency of 9 rad/s in a 6-in.-diameter pipe. A 1/5 scale model is to be used to determine the pressure difference per unit length, Ap, (at any instant) along the pipe. Assume that Api= f(D, Vo, w, t, u, p) where D is the pipe diameter, w the frequency, t the time, the u fluid viscosity, and p the fluid density. If the same fluid is used in the model and the prototype, at what frequency should the model operate? Wm i rad/s

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

Problems H.pdf > Problems H.W: Lecture No.6 Part 2 Q1-(2.4-4, Holland): A fluid of density (p) and dynamic viscosity (u) flows in s.s in a cylindrical pipe of inside diameter (d) with mean linear velocity (u). Derive an expression for the pressure gradient AP/L in terms of p, u, d & u. By dimensional analysis (Note Lect. No.3). Q2-An oil with a viscosity of u= 0.40 N-s/m and density p= 900 kg/m flows in a pipe of diameter d= 0.20m. (a) What pressure drop, pl-p2, is needed to produce a flowrate of Q=2.0x10-5 m/s if the pipe is horizontal with xl=0 and x2=10 m? (b) How steep a hill, part (a), but with pl=p2? (c) For the conditions of part (b), if pl=200 kPa, what is the pressure at section, x3=5 m, where x is measured along the pipe? „must the pipe be on if the oil is to flow through the pipe at the same rate as in II
The pressure drop (Ap) test is carried out using a pipe configuration as illustrated below: Manometer 1 Manometer 2 straight pipe D= 2R R= radius in pipe The pipe data and the flowing fluid are as follows: Pipe: D = 1 cm; L= 100 cm. Fluid: Water, with density (A) = 1000 kg/m"; absolute viscosity (u) = 0.001 kg/im.s); Experimental data is shown as shown in the following table: Task: Ja. Plot the graph of the pressure as a function of the average velocity (V.v). b. Based on the equation for laminar flow in the pipe as follows: Ap = 32VuL, Vavg (m/s) Ap (Pa) 0,001 0,002 0,005 0,01 0,02 0,04 0,06 0,08 0,1 0,12 0,15 0,30 0,62 1,61 3,10 6,10 12,10 20,10 26,00 32,50 38,90 47,20 D Compare the experimental results in the table with the results of calculations using the above equation. Leave a comment. Note: Ap = p1-p2. c. The coefficient of friction (f) in the pipe is formulated as follows: f- 2DAD PL(V.) plot (plot) this distribution of fas a function of the Reynolds number (Re). Re is…
The velocity distribution in a 0.02 m diameter horizontal pipe conveying carbon tetrachloride (specific gravity = 1.59, absolute viscosity = 9.6 x 10-6 Pa sec) is given by the parabolic equation: v(r)=0.01(0.12- r?), where v(r) is the velocity in (m/s) at a distance r in (m) from the pipe center. What is discharge? O a. 3.13 x-8 m3/s O b. None of the mentioned O c. 1.047 x 108 m3/sec O d. 4.97 x 109 m3/sec
Dimensional Analysis and Hydraulic Similitude (fluid mechanics) 1. Water at 60F at 12 ft/s in a 6-in. pipe. (a) For dynamic similarity, determine the velocity of medium fuel oil at 90F flowing in a 12-in. pipe. (b) Determine the diameter of the pipe that should be used if a medium lubricating oil at 70oF if flowing at a velocity of 50 ft/s. find the: a. velocity : ____________________ fps b. diameter : ____________________ in.
Suppose you have crude oil flows through an annulus between two horizontal pipes with the same center, if the velocity distribution, and the average velocity Vavp are expressed by: R R In (R₂/R.) (F)] In- 4μl. R-R ΔΡ SµL R+R In(R./R) Where AP: is the pressure drop through the annulus, u: is the fluid viscosity, L: is the pipe length, R, and R₂: are the inside radius of inner and outer pipes, respectively. Write a program in a script file that calculates the velocity distribution and the average velocity. When the script file is executed, it requests the user to input AP. u. L. R, and R₂ where r has many values between R₁ and R₂. The program displays the inputted values and the calculated average velocity (using fprintf) followed by a table with the values r in the first column and the corresponding values of the velocity distribution in the second column.
The laminar flow of a fluid with a constant viscosity, 4, inside a channel is governed by the following boundary value problem (strong form): d'u dp for y E (0, h) "dy dr u = 0 at y = 0 and y = h vhere u is the fluid velocity and is the pressure drop in the direction of the flow. a) Derive the weak form of the boundary value problem described above.
The force f (t) as seen is applied to a stationary mechanical system, where k =1,036 N/m, b = 1,013 N-s/m, fi =494 N, f2 =866 N. Calculate x(t) in meter at t =7.7 sec? f(t) (N) f2 x(t) b fi 00 f(t) 1 2 3 k massless plate
Water flows without viscous effects from the nozzle, as shown in Figure Q2 (b). The pressure meter shows a reading of 8X.X kPa (gauge/gage), where "XX" is the last 2 digits of your index number (e.g., If XX is 01, then the pressure is 80.1 kPa) and the water jet is exposed to atmospheric pressure. (b) XX-78 (3) Water jet (2) 0.05 m- 0.8 m •(1)L - 8X.X КРа Figure Q2 (b) (i) Determine the flow rate at the nozzle exit and the height, h if viscous effects are negligible and the specific weight of water is 9.8 kN/m². (ii) Based on your working from Q2(b)(i), explain how the pressure at point (1) and water velocity at point (2) should be adjusted to increase the flow rate at the nozzle exit.
In Prob. it would be difficult to solve for Ω because of itappears in all three of the dimensionless pump coefficients.Suppose that, in Prob. 5.61, Ω is unknown but D = 12 cmand Q = 25 m 3 /h. The fluid is gasoline at 20 ° C. Rescale thecoefficients, , to make a plot ofdimensionless power versus dimensionless rotation speed.Enter this plot to find the maximum rotation speed Ωforwhich the power will not exceed 300 W.
(b) The kinematic viscosity of a fluid used for model is one third of the kinematic viscosity of the fluid used for prototype. During testing of the model, if viscosity and gravity forces are predominant, find the scale ration, velocity ratio and discharge ration
The slope of the height h of a surface wave moving in a shallow pool of liquid is related to the speed of the wave u and gravity g by the following equation и ди дх g əx (a) Use a length scale L and a velocity scale Vo to 'nondimensionalize' the equation (b) What is the nondimensional parameter of the flow?
1. Answer the following questions: (a) What is the physical meaning of the following: D a +V.v at Dt where V is the velocity vector of the flow field. (b) Let the viscous stress tensor be denoted by 7. How is the surface (vector) force f, acting by the fluid on a surface element ds (with unit normal în ) computed? Give your answer in vector notation and also in index notation. What is the physical meaning of Ty ? (c) Write down the work done on a material volume of fluid by the viscous surface force in vector notation and also in index notation. (d) Write down the amount of conduction heat flux 'q' (a scalar) on a surface element ds (with unit normal în ) in vector notation and also in index notation.