Cold water enters a pipe where it is heated by an external h

Cold water enters a pipe, where it is heated by an external heat source. The inlet and outlet water temperatures are T_in and T_out, respectively. The total rate of heat transfer Q from the surroundings into the water in the pipe is known to be a function of mass flow rate m \', the specific heat c_p of the water, and the temperature difference between the incoming and outgoing water. Use dimensional analysis to find the functional relationship between these parameters. Represent Q in terms of its fundamental dimensions.

Solution

>> As, Q\' = Total Rate of Heat Transfer

Dimensionally, Speaking, Q\' = Q/t

Q = Heat Transfer or Energy

As, Energy = Force*Distance = mass*acceleration*distance

=> Q = m*(L/t²)*L = m*L²/t²

So, Q\' = Q/t = m*L²/t³ .........thus OPTION (b).........

>> and, as Q\' = m*Cp*dT

So, Q\'/(mCpdT) = constant .....OPTION (b)......