Flow Between Parallel Plates with Spacing 2R - Engineering Assignment Help

Assignment Task :

1. Consider flow between parallel plates with spacing 2R between them. You wish to get an estirnate on the length required for the flow to fully develop. You invoke the concept of the boundary layer on a flat surface and assume that the location where the boundary layers rneet is a reasonable estimate of the entrance length. Assurne the boundary layer to be laminar and with the profile that was assurned in class. At the start of the developed region the boundary layer thickness is half the distance between the plates. Use the centreline velocity as the free strearn velocity and the concept of the displacernent thickness to estimate the inviscid centreline velocity. Assume the velocity at entry is constant at Ili,. The inviscid centreline velocity where the boundary layers meet rnust be close to the fully developed centreline velocity developed in class. 
 

2. Recuperative heaters are used in power stations to extract heat from the exiting hot gas and transfer to the incoming cooler gases. The hot gases transfer heat to a solid matrix which gets heated up and the hot matrix in turn transfers heat to the cooler gases. You assume the rnatrix to resernble spherical particles and rnodel one such system as duct with a large of spherical balls of diameter 'd' to compute the pressure drop in the channel. Assuming that the drag coefficient for spheres is Co and each sphere acts independent of each other compute the pressure d(op(Pi•P)) in the section if the pipe diameter is D and gas density is p. The inlet velocity can be assumed to be U, which is also the velocity that can be used in the drag coefficient expression. Pipe wall shear effects can be ignored and number of balls is N. (10) 
 

3. Water flows in between two parallel plates. The lower plate moves to the left at a speed of 0.5m/s and the upper plate is stationary. The flow is laminar and the spacing between the plates is 5mm. Determine the condition under which the maximum velocity in the flow in between the plates is equal in magnitude to the bottom plate speed i.e. 0.5m/s. Assume the viscosity of water p=9X10 Va-s. Use a coordinate systern starting at the top plate and positive axis pointing towards the bottom plate. You can leave the final solution as an equation or use your machine to get the solution to the nonlinear equation that may result. (10) 
 

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