Cold water enters a pipe, where it is heated by an external heat source. The inl
ID: 2321187 • Letter: C
Question
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.Explanation / Answer
>> 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)......