The entrance flow between two parallel plates (gap h) has a velocity that varies linearly at the entrance and develops into a fully parabolic profile at the exit. What is the relationship between the maximum velocity at the entrance and that at the exit? You can show by symmetry that the maximum velocity is attained at the mid-plane between the two plates.

2. Show that the two-dimensional flow described (in meter-second units) by the equation y = x + 2x² – 2y² is irrotational. What is the velocity potential of the flow? If the density of the fluid is 1.12 kg m and the piezometric pressure at the point (1, -2) is 4.8 kPa, what is the piezometric pressure at the point (9, 6)? -3

The velocity field for a flow is given by: V= (5x+ 6y+ 72) i+ (6x+ 5y + 9z)j + (3x+ 2y + Az)k -21 and the density varies es p = Po e. In order that the mass is conserved, the value of A should be

You must have a diagram to show the force. Provide answer in detailed way

show all work

Find the stagnation point in the following two-dimensional velocity field: V=(3+x-y)i + (5+x+y)j

The velocity components of an incompressible, two-dimensional field are given bythe following equations:  u(x,y) =y^2 -x (1+x) v(x,y) = y(2x+1) Show that the flow field is (a) irrotational and (b) satisfies conservation of mass.

A water jet with volume flow rate of 3 m³/s is moving in the positive x- direction at a speed of 6 m/s. The stream hits a stationary splitter, such that half of the flow is diverted upward at 45º and the other half is directed downward at 45°, and both streams have a final average speed of 6 m/s. The gravitational effects and friction loss are considered to be negligible. Determine the x- and z-components of the force required to hold the splitter in place against the water force. Note that the pressure of the water jet at inlet and outlet sections is the atmospheric pressure and the density of water is taken as 1000 kg/m³. 3 m³/s 6 m/s 45° A 45° Figure 3.1 2 FR: FRX

A Newtonian fluid is flowing in the narrow gap between two infinite parallel horizontal plates due to the movement of the top plate (see the figure below). The top plate is moving at a speed U from left to right, and the bottom plate is stationary. Consider the flow is steady, incompressible, and laminar. The distance between two plate is H, and the gravity acts in negative z-direction (which is perpendicular into the page). There is an applied constant pressure gradient of apJəx in the x-direction. Calculate the velocity and pressure fields. Plot typical velocity profiles in dimensionless form for a pressure gradient value of 0 and -15. In your solution show the conceptual diagram of the problem; write all relevant assumptions and boundary conditions; show the detailed steps of the problem solutions including equations and detailed processing of those equations. Moving plate Fluid: p.H Fixed plate P2-P1

A cylinder is formed by bolting two semicylindrical channelstogether on the inside, as shown in Fig.  Thereare 10 bolts per meter of width on each side, and the insidepressure is 50 kPa (gage). Using potential theory for theoutside pressure, compute the tension force in each bolt ifthe fluid outside is sea-level air.