Problem 1CP: The divergence theorem is v.cdv=A c . n dA Problem 2CP: Explain the fundamental differences between a flow domain and a control volume. Problem 3CP: What does it mean when we say that two more differential equations are coupled? Problem 4CP Problem 5CP Problem 6CP Problem 7P Problem 8P Problem 10P: Let vector G=2xzi12x2jz2kk . Calculate the divergance of G , and simplify as much as possible, Is... Problem 11P Problem 12P Problem 13P Problem 14P Problem 15P Problem 16P Problem 17P Problem 18EP: Alex is measuring the time-averaged velocity components in a pump using a laser Doppler velocimeter... Problem 19P: Let vector c be given G=4xziy2i+yzkand let V be the volume of a cube of unit length with its corner... Problem 20P: The product rule can be applied to the divergence to the divergence of scalar f times vector G as:... Problem 21CP: In this chapter we derive the continuity equation in two way: by using the divergence theorem and by... Problem 22P Problem 23P: Repeat Example 9-1(gas compressed in a cylinder by a piston), but without using the continuity... Problem 24P: The compressible from of the continuity equation is (/t)+(V)=0 . Expand this equation as far... Problem 25P: In Example 9-6 we derive the equation for volumetric stain rate, (1/V)(DV/Dt)=V . Write this as a... Problem 26P: Verify that the spiraling line vortex/sink flow in the r -plane of Prob. 917 satisfies the... Problem 27P: Verify that the steady; two-dimensional, incompressible velocity filed of Prob. 9-13 satisfies the... Problem 28P Problem 29P: Consider steady flow of water through an axisymmetric garden hose nozzle (Fig. 9-28). Suppose the... Problem 30P: Consider the following steady, three-dimensional velocity field in Cartesian coodinates:... Problem 31P: Consider the following steady, three-dimensional velocity field in Cartesian coordinates:... Problem 32P: The u velocity component of a steady, two-dimensional, incompressible flow field is u=ax+b ,where a... Problem 33P: Imagine a steady, two-dimensional, incompressible flow that is purely circular in the xy-or rplane .... Problem 34P Problem 35P: The u velocity component of a steady, two-dimensional, incompressible flow is u=3ax22bxy , where a... Problem 36P: Imagine a steady, two-dimensional, incompressible flow that is purely radial in the xy-or- r -plane.... Problem 37P: Two velocity components of a steady, incompressible flow field are known: u=2ax+bx+cy2 and v=azbyz2... Problem 39CP Problem 40CP: In CFD lingo, the stream function is often called a non-primitive variable, while velocity and... Problem 41CP Problem 42CP: What is significant about curves of constant stream function? Explain why the stream function is... Problem 43P Problem 44P Problem 46P Problem 47P: As a follow-up to Prob. 9-45, calculate the volume flow rate per unit width into the page of Fig.... Problem 48EP: Consider the Couette flow of Fig.9-45. For the case in which V=10.0ft/s and h=1.20in, plot several... Problem 49P Problem 50P: AS a follow-up to Prob. 9-48, calculate the volume flow rate per unit width into the page of Fig.... Problem 51P: Consider the channel flow of Fig. 9-45. The fluid is water at 20C . For the case in which... Problem 52P: In the field of air pollution control, one often needs to sample the quality of a moving airstream.... Problem 53P: Suppose the suction applied to the sampling prob.9-51 were too weak instead strong. Sketch what the... Problem 54P Problem 55P Problem 56P Problem 57P Problem 58P Problem 60P Problem 61P Problem 62P Problem 63P Problem 64EP Problem 65P Problem 66EP Problem 67P: Flow separates at a shap corner along a wall and froms a recirculating and a recirculating separtion... Problem 69P Problem 70EP Problem 71P Problem 72P Problem 74P Problem 75P Problem 76P Problem 77P Problem 78CP Problem 79CP: What are constitutive equations, and to the fluid mechanics equation are applied? Problem 80CP: An airplane flies at constant velocity Vairplane (Fig. P9-79C). Dissuss the velocity boundary... Problem 81CP: Wht in the main distionction between Newtormine fluid and a non-Newtonian flud? Name at lest three... Problem 82CP: Define or describe each type of fluid: (a) viscoelastic fluid (b) pseudoplastic fluid (c) dilatant... Problem 83CP: The general cool volume from of linearmomentum equation is CVgdV+csijndA= cv t( V)dV+ CS( V)VndA... Problem 84P: Consider liquid in a cylindrical tank. Both the tank and the liquid rotate as a rigid body (Fig.... Problem 85P Problem 86P: Engine oil at T=60C is forced to flow between two very large, stationary by a thin gap height... Problem 87P: Consider the steady, two-dimensional, incompressible velocity field, V=(u,v)=(ax+b)i+(ay+c)j, where... Problem 88P: Consider the following steady, two-dimensional, incompressible velocity field:... Problem 89P: Consider steady, two-dimensional, incompressible flow due to a spiraling line vortex/sink flow... Problem 90P: Consider the following steady, two-dimensional, incompressible velocity field:... Problem 91P: Consider steady, incompressible, parallel, laminar flow falling between two infinite vertical walls... Problem 92P Problem 93P Problem 94P Problem 95P: The first viscous terms in -comonent of the Navier-Stokes eqation (Eq.9-62c) are [1rr(rur)gr2] .... Problem 96P: An incompressible Newtonian liquid is confined between two concentric circular cylinders of infinite... Problem 97P Problem 98P Problem 99P Problem 100P Problem 101P: Consider steady, incompressible, laminar flow of a Newtonian fluid in an infinitely lons round pipe... Problem 102P: Consider again the pipe annulus sketched in Fig 9-98. Assume that the constant everywhere (there is... Problem 103P: Repeat Prob. 9-99 except swap the stationary and moving cylinder. In particular, let the inner... Problem 104P: Consider a modified form of Couette flow in which there are two immiscible fluids sandwiched between... Problem 105P: Consider steady, incompressible, laminar flow of a Newtonian fluid in an infinitely long round pipe... Problem 106P Problem 107P Problem 108CP Problem 109CP Problem 110CP Problem 111CP Problem 112P: Discuss the relationship between volumetric strain rate and the continuity equation. Base your... Problem 113P Problem 114P Problem 116P Problem 117P Problem 118P Problem 119P Problem 120P: For each of the listed equation, write down the equation in vector from and decide if it linear or... Problem 121P Problem 122P Problem 123P: A block slides down along, straight inclined wall at speed V,riding on a thin film of oil of... Problem 124P: Look up the definition of Poisson’s equation in one of your math textbooks or on the Internet. Write... Problem 125P: Water flows down a long, straight, inclined pipe of diameter D and length L (Fig. 9-123). There is... Problem 127P Problem 128P Problem 129P: The Navier-Stokes equation is also known as (a) Newton’s first law (b) Newton’s second law (c)... Problem 130P: Which choice is the genera1 differential equation form of the continuity equation for a control... Problem 131P: Which choice is the differential , incompressible, two-dimensional continuity equation in Cartesian... Problem 132P: A steady velocity field is given by V=(u,v,w)=2ax2yi+3bxy2j+cyk , where a, b, and c are constants.... Problem 133P: A steady, two-dimensional, incompressible flow field in the xy-plane has a stream function given by... Problem 134P: A steady, two-dimensional, incompressible flow field in the xy-plane has a stream function given by... Problem 135P Problem 136P Problem 137P: Which choice is not correct regarding the Navier-Stokes equation? (a) Nonlinear equat3n (b) Unsteady... Problem 138P: In thud flow analyses, which boundary condition can be expressed as Vfluid=Vwall? (a) No-slip (b)... format_list_bulleted