A cylinder of mass $$10$$ kg and area of cross-section $$0.1$$ $${m^2}$$ is tied down with string in a vessel containing two liquids as shown in Figure. Calculate gauge pressure on the cylinder bottom and the tension in the string. Density of water $$ = 1000\,\,kg/{m^3}.$$ Specific gravity of $$A=0.8$$. Specific gravity of $$B$$ (water) $$=1.0$$

Hot water flows with a velocity of $$0.1$$ $$m/s$$ in a $$100mm$$ long, $$0.1m$$ diameter pipe. Heat lost from the pipe outer wall is uniform and equal to $$420$$ $$W/{m^2}$$. If the inlet water temperature is $${80^ \circ }C,$$ calculate the water temp at the exit. Neglect effect of pipe wall thickness. $${C_p}$$ (water) $$=4.2$$ $$kJ/kg$$-$$K$$ and density of water $$=1000$$ $$kg/\,{m^3}.$$

A hot fluid at $${200^ \circ }C$$ enters a heat exchanger at a mass flow rate of $${10^4}\,\,kg/hr.$$ Its specific heat is $$2000$$ $$J/kg$$-$$K.$$ It is to be cooled by another fluid entering at $${25^ \circ }C$$ with a mass flow rate $$2500$$ $$kg/hr$$ and specific heat $$400$$ $$J/kg$$-$$K$$. The overall heat transfer coefficient based on outside area of $$20\,\,{m^2}$$ is $$250\,\,\,W/{m^2}K.$$ Find the exit temperature of the hot fluid when the fluids are in parallel flow.

Heat transfer coefficients for free convection in gasses, forced convection in gases and vapors, and for boiling water lie, respectively, in the range of