The velocity components in the $$x$$ and $$y$$ directions are given by $$u = \lambda x{y^3} - {x^2}y,$$ $$v = x{y^2} - {3 \over 4}{y^4}.$$ The value of $$\lambda $$ for a possible flow field involving an incompressible fluid is

The force $$F$$ needed to support the liquid of density $$d$$ and the vessel on top (fig) is

In fully developed laminar flow in the circular pipe, the head loss due to friction is directly proportional to ....... (Mean velocity/square of the mean velocity)

Consider two large parallel plates, one at $${T_1} = {727^ \circ }C$$ with emissivity $${\varepsilon _1} = 0.8$$ and the other at $${T_2} = {227^ \circ }C\,$$ with emissivity $${\varepsilon _2} = 0.4.$$ An aluminium radiation shield with an emissivity, $${\varepsilon _s} = 0.05$$ on both sides is placed between the plates. Calculate the percentage reduction in heat transfer rate between the two plates as a result of the shield.
Use $$\sigma = 5.67 \times {10^{ - 8}}W/\left( {{m^2}{K^4}} \right)$$