A Prandtl tube (Pitot-static tube with $$C=1$$) is used to measure the velocity of water. The differential manometer reading is $$10$$ mm of liquid column with a relative density of $$10.$$ Assuming $$g = 9.8\,\,m/{s^2},$$ the velocity of water (in $$m/s$$) is ___________

Three parallel pipes connected at the two ends have flow-rates $$\,\,\,{Q_1},\,\,\,{Q_2},\,\,\,\,$$ and $${Q_3}$$ respectively, and the corresponding frictional head losses are $${h_{L1}},\,\,\,{h_{L2}},$$ and $${h_{L3}}$$ respectively. The correct expressions for total flow rate $$(Q)$$ and frictional head loss across the two ends $$\left( {{h_L}} \right)$$ are.

Couette flow is characterized by

A brick wall $$\,\left( {k = 0.9{W \over {m.K}}} \right)$$ of thickness $$0.18$$ $$m$$ separates the warm air in a room from the cold ambient air. On a particular winter day, the outside air temperature is −$${5^ \circ }C.\,$$ and the room needs to be maintained at $${27^ \circ }C.\,$$ The heat transfer coefficient associated with outside air is $$20\,\,W/{m^2}K.$$ Neglecting the convective resistance of the air inside the room, the heat loss, in $$\left( {{W \over {{m^2}}}} \right)$$ is