Oil in a hydraulic cylinder is compressed from an initial volume $$2{m^3}$$ to $$1.96{m^3}$$. If the pressure of oil in the cylinder changes from $$40$$ $$MPa$$ to $$80$$ $$MPa$$ during compression, the bulk modulus of elasticity of oil is .........

Newton's law of viscosity states that the shear stress in a fluid is proportional to :

The temp distribution within the Laminar thermal boundary layer over a heated isothermal flat plate is given by
$$\left( {T - {T_w}} \right)/\left( {{T_\infty } - {T_w}} \right) = \left( {3/2} \right)\,\,\left( {y/{\delta _t}} \right) - \left( {1/2} \right){\left( {y/{\delta _t}} \right)^3},$$
where $${{T_w}}$$ and $${{T_ \propto }}$$ are the temp of plate and free stream respectively, and $$'y'$$ is the normal distance measuread from the plate. The ratio of Average to the local Nussult number based on the thermal boundary layer thickness $${{\delta _t}}$$ is given by

In a counter flow heat exchanger, hot fluid enters at $${65^ \circ }C$$ and cold fluid leaves at $${30^ \circ }C.$$ mass flow rate of the hot fluid is $$1$$ $$Kg/s$$ and that of cold fluid is $$2$$ $$kg/s$$. Specific heat of the hot fluid is $$10$$ $$kgK$$ and that of cold fluid is $$5$$ $$kj/kgK.$$ The $$LMTD$$ for the heat ecchanger is