1. When a uniform stream flows past an immersed thick cylinder, a broad low-velocity wake is created downstream, idealized as a V shape in Fig. 1. Pressures p1 and p2 are approximately equal. (a) If the flow is two-dimensional and incompressible, with width b into the paper, derive a formula for the drag force F on the cylinder. (b) Rewrite your result in the form of a dimensionless drag coefficient based on body F pU²bL length Cp: =

1. When a uniform stream flows past an immersed thick cylinder, a broad low-velocity wake is created downstream, idealized as a V shape in Fig. 1. Pressures p1 and p2 are approximately equal. (a) If the flow is two-dimensional and incompressible, with width b into the paper, derive a formula for the drag force F on the cylinder. (b) Rewrite your result in the form of a dimensionless drag coefficient based on body F pU²bL length Cp: =

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

When a uniform stream flows past an immersed thick cylinder, a broad low-velocity wake is created downstream, idealized as a V shape in Fig. 1. Pressures p1 and p2 are approximately equal. (a) If the flow is two-dimensional and incompressible, with width b into the paper, derive a formula for the drag force F on the cylinder. (b) 1. Rewrite your result in the form of a dimensionless drag coefficient based on body F length Cp pU²bL U = L Fig.1. Airflow on a cylinder U U U/2 L/2 L/2
U L CD Fig.1. Airflow on a cylinder U U U/2 L/2 L/2 1. When a uniform stream flows past an immersed thick cylinder, a broad low-velocity wake is created downstream, idealized as a V shape in Fig. 1. Pressures p1 and p2 are approximately equal. (a) If the flow is two-dimensional and incompressible, with width b into the paper, derive a formula for the drag force F on the cylinder. (b) Rewrite your result in the form of a dimensionless drag coefficient based on body length F pU²bL
QUESTION: (ii) Use Buckingham's theorem to obtain in dimensionless form an expression for the force acting on a smooth sphere placed in an incompressible viscous flow filed .
Consider laminar flow through a long section of pipe, as in Fig. For laminar flow it turns out that wall roughness is not a relevant parameter unless ? is very large. The volume flow rate V· through the pipe is a function of pipe diameter D, fluid viscosity ? , and axial pressure gradient dP/dx. If pipe diameter is doubled, all else being equal, by what factor will volume flow rate increase? Use dimensional analysis.
Algebraic equations such as Bernoulli's relation, are dimensionally consistent, but what about differential equations? Consider, for example, the boundary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: ди ди ap ат ри — + pu Әх + pg: + дх ày ду where T is the boundary-layer shear stress and g, is the com- ponent of gravity in the x direction. Is this equation dimen- sionally consistent? Can you draw a general conclusion?
Oil, of density ρ and viscosity μ , drains steadily down theside of a vertical plate, as in Fig. P4.80. After a developmentregion near the top of the plate, the oil fi lm willbecome independent of z and of constant thickness δ .Assume that w = w ( x ) only and that the atmosphere offersno shear resistance to the surface of the fi lm. ( a ) Solve theNavier-Stokes equation for w ( x ), and sketch its approximateshape. ( b ) Suppose that fi lm thickness δ and the slopeof the velocity profi le at the wall [ ∂ w /∂ x ] wall are measuredwith a laser-Doppler anemometer (Chap. 6). Find anexpression for oil viscosity μ as a function of ( ρ , δ , g ,[ ∂ w / ∂ x ] wall ).
1- Reynolds number is a dimensionless number represent .....to .. 2- The velocity profile of the flow between two parallel plates is linear if the pressure gradient equal and parabolic if the pressure gradient has a .... 3- In the sink and source flow the potential function is represented as.. ...... and the stream function is represented as **** 4- In the laminar boundary layer, the .............. is the dominant reason for the loss while in turbulent boundary layer the is dominant. 5- For inviscid flow, there are no shear stresses the only forces acting on a fluid element are ....... and. *****
A milkshake has fairly similar density to that of water (m s = 1200 kg/m3) but is far more viscous ( = 1kg/ms) (a) Say you try to drink a milkshake through a straw that is 30 cm long and 5 mm in diameter. Your lungs are capable of creating a vacuum pressure of 3000 Pa. (Vacuum pressure just means a pressure below that of the atmosphere, so plung = patm 3000 Pa.) You Önd that if you place the straw just at the surface of the liquid, you are unable to suck the milkshake through the straw, but if you push the straw deeper into the shake, you can. To what depth, d, would you need to push the straw in order to just start to sip the milkshake?(b) Suppose you push the straw to a depth of 10 cm and suck with a suction pressure of 3000 N/m2. What volume áow rate of milkshake can you produce through the straw
(a) In a variety of environmental problems, it is common to find fluid motions that have a cellular character; i.e. the fluid streamlines form closed loops in the form of a cell. An example of a 2D cellular flow is ū = sin(rx) cos(ry)î – cos(rx) sin(ry)j (i) Is this flow incompressible? (Justify you answer.) (ii) Calculate the vorticity. (iii) Where is the magnitude of the vorticity highest, and where does it vanish?
A viscous liquid of constant ρ and μ falls due to gravitybetween two plates a distance 2 h apart, as in Fig. P4.37. Thefl ow is fully developed, with a single velocity component w = w ( x ). There are no applied pressure gradients, onlygravity. Solve the Navier-Stokes equation for the velocityprofi le between the plates.
Flat Couette Flow An incompressible fluid of viscosity n is located between two plates infinite, spaced 2d. The top plate has velocity V x and the bottom plate low - V x*. (Gravity is neglected and pressure is constant.) YA +d -d -Va X +Vâ (a) Calculate the velocity of the fluid. (b) Sketch the forces acting on the fluid and calculate them.
3.4 Specification of a laminar boundary layer profile as an inflow condition is often used in incompressible flow simulations. Let us consider the Blasius profile, which is a similarity solution for the steady laminar boundary layer on a flat plate. Fig. 3.25 Flat-plate laminar boundary layer Dv 2. Consider the streamfunction(with u = and v=- transform from (x, y) to (x, n), where n = y √ux/U% = Rex u(x, y) and a coordinate Using the above and a streamfunction in the form = √xUf(n), show that the governing equations can be reduced to ff" +2f"" = 0 with boundary conditions of f(0) = f'(0) = 0 and lim, f(n) = 1. This equation is referred to as the Blasius equation and its solution is known as the Blasius profile.