A 30 kW heat emitter has a flow water temperature of 82^oC while return water leaves at 71^oC. Specific heat capacity of water is 4.2 kJ/kg K. Pipe heat emission amounts to 10% of emitter output. Which of these is the water flow rate?

Question

Quizplus · Accepted Answer

We can use the following formula to calculate water flow rate:

$\dot{Q}=\dot{m} c_p \Delta T$

where:

$\dot{Q}$ = heat output of emitter = 30 kW
$\dot{m}$ = mass flow rate of water
$c_p$ = specific heat capacity of water = 4.2 kJ/kg K
$\Delta T$ = temperature difference = (82 - 71) = 11 °C

We also know that pipe heat emission is 10% of the emitter output, so the total heat output is:

$\dot{Q}_{total} = 1.1 \dot{Q}$

Substituting the values:

$\dot{Q}_{total} = 1.1 	imes 30 = 33 kW$

Now, we can use the formula to calculate mass flow rate:

$\dot{m} = \frac{\dot{Q}_{total}}{c_p \Delta T}$

Substituting the values:

$\dot{m} = \frac{33 	imes 10^3}{4.2 	imes 11} = 722.2 	ext{ kg/h}$

Converting to kg/s:

$\dot{m} = \frac{722.2}{3600} = 0.2 	ext{ kg/s}$

Therefore, the water flow rate is 0.72 kg/s, which is the closest option to our calculated value.

A 30 KW Heat Emitter Has a Flow Water Temperature