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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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INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
- force in three dimensions is given by (a) F = FO(yx^ - xy^) (b) F= FO(yx^ + xy ^) where x^ and y^ are the cartesian basic vectors and F0 is a constant. Find if possible the corresponding potential energyarrow_forwardWater at T = 20°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r).arrow_forward3.3. 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_forward
- 4. Kittel Ch3-4. Energy fluctuations. Consider a system of fixed volume in thermal contact with a reservoir. Show that the mean square fluctuation in the energy of the system is ((x − (e))²) = t² (əU / ət), Here U is the conventional symbol for (e). Hint: Use the partition function Z to relate U/ar to the mean square fluctuation. Also, multiply out the term (...). (89)arrow_forwardEngine oil at 60°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r). (Hint: P = Patm everywhere on the free surface. The flow is rotationally symmetric about the z-axis.)arrow_forwardi need the answer quicklyarrow_forward
- 1. Derive the 3rd Order, non-linear, Blasius equation, as shown in class F"" + 1/2 FF" =0arrow_forward2) If k=m=b=1 is the system Controllable?arrow_forwardIn the Fig. is shown the cross-section of the tank full of water under pressure. The length of the tank is 2.5 m. An empty cylinder lies along the length of the tank on one of its corners as shown. Find the horizontal and vertical components of the force acting on the curved surface LMN of the cylinderarrow_forward
- Select the correct combination, which are the examples of vector quantities. Distance , Displacement O Force , Pressure O Distance, Density O Moment, Momentumarrow_forwardi need the answer quicklyarrow_forwardAccess plates on the industrial holding tank are bolted shut when the tank is filled with vegetable oil as shown. Suppose that h=7m and d= 1.9m rho_vo=932 kg/m^3. Use the formula method to determine the resultant force that the liquid exerts on plate B and the location of the resultant force from the bottom of the tank.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