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In the two-dimensional body illustrated, the gradient at surface A is found to be
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Introduction to Heat Transfer
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- 3.3. The velocities at a point in a fluid in the Eulerian system are given by ux+y+z+s =2(x + y + z) +- 1 W = 3(x + y + z) + i Show that the displacements of a fluid particle in the Lagrangian system are x=2x-30 120 + f (x + y + zo + 1')e" - r²+++ - - y= -xo+yo-zo + (xo + yo + zo + 1)e³ - f - 38 z = −x − y + zo + (x + yo +20 + 1)e" - 11 - 11² - 2 -arrow_forwardQ2- 21 The velocity distribution in the boundary layer is given by: U y 8 is the velocity at a distance y from the plate and u = U aty = 8,8 being boundary layer thickness. Find : (i) The displacement thickness, (ii) The momentum thickness, where 24arrow_forwardbut change the spring constant (k) of spring DB to 310 N/marrow_forward
- Exercise 1 At a certain point of a body, the components of the cauchy stress tensor are given by [2 5 3 [o] 5 1 4 3 4 3 a) Find the components of cauchy traction vector tn at the point on the plane whose normal has direction (3, 1, –2). b) Find the normal and shear commponents of tn on that point.arrow_forward1. Derive the 3rd Order, non-linear, Blasius equation, as shown in class F"" + 1/2 FF" =0arrow_forwardProblem 2: The potential energy for a particular two-dimensional force field is given by V(x, y) = Axe-ky, where the constants A and k are chosen for dimensional consistency. (a) Choose specific (and reasonable) values for A and k, and use Mathematica, Desmos, or the equivalent to plot contours of constant potential energy for various energy levels, over a region of the plane centered on the origin. (b) Show that an infinitesimal displacement along an equipotential line has the form dr dr = dr x + ŷ. kx (c) Find the expression for the force field, and plot this vector field over the same region of the plane (and with the same choice of constants) as in part (a).arrow_forward
- 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the differential equation d²y + y = 0 dx2 Hence, find the solution of this equation subject to the following boundary conditions y(0) = 1, = 1 (cos, sin) S A Unit Circle sin tan = Quadrant II: cos Quadrant I: - + + (0, 1) 2'2 2 2'2 90° 120° 60° 4 135° 45° 150° 30° 180° 0° (-1,0) (1, 0) 360° 210° 330° 117 6 (목) 225° 315° 240° 300° 4 270° 3 2 2 2 (0, –1) C Quadrant Ill: Quadrant IV: 프_3arrow_forwardFor a constant tensor, Ajk prove that V(Ag x, X )= (Ay + Ag )x,.arrow_forwardThe constants are evaluated using the boundary conditions.True or false?arrow_forward
- The double acting cylinder that converts the fluid energy into mechanical energy in the form of linear movement in directions. O Three O Two O No O Onearrow_forwardIn the image given below, determine Ap between points A and B, when x = 15 cm. All fluids are at 20°C. Air Benzene 40 cm 07-19 48 c cm Kerosene Mercury- Water Take the specific weights to be Benzene: 8640 N/m³ Mercury: 133100 N/m³ Kerosene: 7885 N/m³ Water: 9790 N/m³ Pressure difference = Pa 19 cm 14 cmarrow_forwardThe centre of gravity of the following shown area OBC, where the curve OC is given by the equation y=0.625x, with respect to the point O (0, 0) is: yA -4 HB (A) (6,5) ) (3.5) (В) (6, 3) (D) (3, 3)arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage LearningInternational Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L