The stream function in a two dimensional flow field is given by $$\Psi = {x^2} - {y^2}$$
The magnitude of the velocity at point $$(1,1)$$ is

A $$400m$$ long horizontal pipe is to deliver $$900$$ kg of oil
$$\left( {S = 0.9,\,\,\upsilon = 0.0002{m^2}/s} \right)$$ per minute. If the head loss is not to exceed $$8$$ $$m$$ of oil, find the pipe diameter.

(Friction factor in laminar flow: $$f = 64/{R_e}$$)

In a syringe as shown in the figure, a piston of $$1\,\,c{m^2}$$ cross section is pushed at a constant speed of $$10\,\,cm/s$$ to eject water through an outlet of $$1\,\,m{m^2}.$$ Determine the force required to move the piston. Neglecting losses.

The heat transfer process between a body and its ambient is governed by an internal conductive resistance $$\left( {{\rm I}CR} \right)$$ and an external convective resistance $$(ECR).$$ The body can be considered to be a lumped heat capacity system if