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As writing these equations gets tedious on keyboard, i am posting my hand written notes.I Hope its legible and easy to understand.
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Repeat the flat-plate momentum analysis by replacing the equation u(x, y) ~U ( ) 0<y>$(x) using...
Question 3: --うつc A flat plate is inserted with its edge at x = 0 in...
Question 3: --うつc A flat plate is inserted with its edge at x = 0 in a uniform flow coming at velocity U parallel to the plate from the region where x < 0. If using a cubic approximation to the Blasius profile: u U(2n- n) with n-y/o, in which o(x)- Ax/(Re.) is the boundary layer thickness, 1. What should the relationship be between this δ(x) and the δ99-5.0d(Re.)12 in the Blasius profile, in order to yield the same drag?...
1- Consider laminar flat plate flow with the following approximate velocity profile: U[ exp-5y/8)] which satisfies the...
1- Consider laminar flat plate flow with the following approximate velocity profile: U[ exp-5y/8)] which satisfies the conditions u = 0.993U at y = S. (a) Use this 0 at y 0 and u= profile in the two-dimensional momentum integral relation to evaluate the approximate boundary layer thickness variation S(x). Assume zero pressure gradient. (b) Now explain why your result in part (a) is deplorably inaccurate compared to the exact Blasius solution Scanned uww Cam Scanner
1- Consider laminar flat...
Solve the equation yu- xui = u, t > 0,x >0 with the initial conditions u(x,...
Solve the equation yu- xui = u, t > 0,x >0 with the initial conditions u(x, 0) =1 + x2 using the method of characteristics. Find the u(x, y). Substitute your found solution u(x, y) in the equation and verify that it satisfies the equation. solution explicitly in the form u =
= A square plate is bounded by x = 0, x = a, y = 0...
= A square plate is bounded by x = 0, x = a, y = 0 and y = a. Apply the Laplace's equation əzu 22u + = 0 дх2 ду2 to determine the potential distribution u(x,y) over the plate, subject to the following boundary conditions u(0, y) = 0, uſa, y) = 0, 0<y <a πχ 2πχ u(x,0) = 0, u(x, a) = u, (sin + 2 sin 0 < x < a, where uo is a constant. Also...
Problem #3 Air flows over a flat plate at 4 m/s. An approximation for the x...
Problem #3 Air flows over a flat plate at 4 m/s. An approximation for the x component of velocity in the in- compressible laminar boundary layer is a sinusoidal variation from u-0 at the surface (y-0) to the freestream velocity, U, at the boundary-layer edge (y-5). The equation for the profile is u-Usin( %), where cVx and c is a constant. The boundary layer is 9 mm thick 1 m from the edge of the plate. (a) Predict the boundary-layer...
22. Consider the momentum integral equation turbulent boundary layer on an isothermal flat plate. The boundary...
22. Consider the momentum integral equation turbulent boundary layer on an isothermal flat plate. The boundary layer is tripped at x-0. Assume constant properties and velocity. An experiment conducted to measure u and τ showed that for a steady, and τ= 0.0228 ρu® a) Determine the local friction coefficient, Cf/2 b) Using Colburn analogy, obtain an expression for the local Nusselt number.
JESTION 3 [15 MARKS nsider a flow along a flat plate with a boundary layer profile...
JESTION 3 [15 MARKS nsider a flow along a flat plate with a boundary layer profile given by: u 3 y ang Von-Karman momentum integral equation method, determine the value of: i. boundary layer momentum thickness, 0/8 ii. boundary layer thickness, 8x iii. boundary layer displacement thickness. 8*x (15
A flat plate has an area D specified by the constraints y> 0 and 1 <...
A flat plate has an area D specified by the constraints y> 0 and 1 < x2 + y2 <16. If the density is given by p(x, y) = y y (22 +32) then the mass of the plate is given by the double integral SJ p(,y) dedy D Evaluate the double integral using polar coordinates z=r cos (O) and y=r sin (O). SJ p(x,y) d.ody= D Preferably leave you answer in terms of fractions, exponentials or 7. If you...
PROBLEM 4.3. The one-dimensional wave equation is ə?u - 20u = 0, ət2 or where c>...
PROBLEM 4.3. The one-dimensional wave equation is ə?u - 20u = 0, ət2 or where c> 0 is constant. Show that any function of the form u(x, t) = f(x - ct)+9(2+ct), where f,g: RR are twice continuously differentiable, satisfies this equation. Explain why we call c the wave speed.
5. Consider a particle moving in the region x>0 under the influence of the potential U(x)...
5. Consider a particle moving in the region x>0 under the influence of the potential U(x) = C (a/x + x/a), where C=1J, and a=2m. (a) Find the equilibrium positions and determine whether they are stable or unstable. (b) Find U at those equilibrium positions. (c) Sketch U(x) without using a computer (explain how you get the sketch) and discuss the motion of the particle in details in all the different regions if its total energy E1 = 2 J,...
Question 3: --うつc A flat plate is inserted with its edge at x = 0 in a uniform flow coming at velocity U parallel to the plate from the region where x < 0. If using a cubic approximation to the Blasius profile: u U(2n- n) with n-y/o, in which o(x)- Ax/(Re.) is the boundary layer thickness, 1. What should the relationship be between this δ(x) and the δ99-5.0d(Re.)12 in the Blasius profile, in order to yield the same drag?...
1- Consider laminar flat plate flow with the following approximate velocity profile: U[ exp-5y/8)] which satisfies the conditions u = 0.993U at y = S. (a) Use this 0 at y 0 and u= profile in the two-dimensional momentum integral relation to evaluate the approximate boundary layer thickness variation S(x). Assume zero pressure gradient. (b) Now explain why your result in part (a) is deplorably inaccurate compared to the exact Blasius solution Scanned uww Cam Scanner
1- Consider laminar flat...
Solve the equation yu- xui = u, t > 0,x >0 with the initial conditions u(x, 0) =1 + x2 using the method of characteristics. Find the u(x, y). Substitute your found solution u(x, y) in the equation and verify that it satisfies the equation. solution explicitly in the form u =
= A square plate is bounded by x = 0, x = a, y = 0 and y = a. Apply the Laplace's equation əzu 22u + = 0 дх2 ду2 to determine the potential distribution u(x,y) over the plate, subject to the following boundary conditions u(0, y) = 0, uſa, y) = 0, 0<y <a πχ 2πχ u(x,0) = 0, u(x, a) = u, (sin + 2 sin 0 < x < a, where uo is a constant. Also...
Problem #3 Air flows over a flat plate at 4 m/s. An approximation for the x component of velocity in the in- compressible laminar boundary layer is a sinusoidal variation from u-0 at the surface (y-0) to the freestream velocity, U, at the boundary-layer edge (y-5). The equation for the profile is u-Usin( %), where cVx and c is a constant. The boundary layer is 9 mm thick 1 m from the edge of the plate. (a) Predict the boundary-layer...
22. Consider the momentum integral equation turbulent boundary layer on an isothermal flat plate. The boundary layer is tripped at x-0. Assume constant properties and velocity. An experiment conducted to measure u and τ showed that for a steady, and τ= 0.0228 ρu® a) Determine the local friction coefficient, Cf/2 b) Using Colburn analogy, obtain an expression for the local Nusselt number.
JESTION 3 [15 MARKS nsider a flow along a flat plate with a boundary layer profile given by: u 3 y ang Von-Karman momentum integral equation method, determine the value of: i. boundary layer momentum thickness, 0/8 ii. boundary layer thickness, 8x iii. boundary layer displacement thickness. 8*x (15
A flat plate has an area D specified by the constraints y> 0 and 1 < x2 + y2 <16. If the density is given by p(x, y) = y y (22 +32) then the mass of the plate is given by the double integral SJ p(,y) dedy D Evaluate the double integral using polar coordinates z=r cos (O) and y=r sin (O). SJ p(x,y) d.ody= D Preferably leave you answer in terms of fractions, exponentials or 7. If you...
PROBLEM 4.3. The one-dimensional wave equation is ə?u - 20u = 0, ət2 or where c> 0 is constant. Show that any function of the form u(x, t) = f(x - ct)+9(2+ct), where f,g: RR are twice continuously differentiable, satisfies this equation. Explain why we call c the wave speed.
5. Consider a particle moving in the region x>0 under the influence of the potential U(x) = C (a/x + x/a), where C=1J, and a=2m. (a) Find the equilibrium positions and determine whether they are stable or unstable. (b) Find U at those equilibrium positions. (c) Sketch U(x) without using a computer (explain how you get the sketch) and discuss the motion of the particle in details in all the different regions if its total energy E1 = 2 J,...
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