Question

An engine is tested by means of a water brake at 1000 rpm. The measured torque of the engine is 10000 Nm and the water consumption of the brake is 0.5 m3 /s, its inlet temperature being 20°C. 

Calculate the water temperature at exit, assuming that the whole of the engine power is ultimately  transformed into heat which is absorbed by the cooling water.

Answer 1

$n=1000~rpm=16.67~rps,$

$M=10000~Nm,$

$K=\frac VT=0.5~\frac{m^3}{s},$

$t_1=20°C,$

$\rho=1000~\frac{kg}{m^3},$

$c=4200~\frac{J}{kg\cdot°C}.$

$Q=cm(t_2-t_1)=PT,$

$P=M\omega,$

$cm(t_2-t_1)=M\omega T,$

$m=\rho V,~\omega=2\pi n,$

$t_2-t_1=\frac{2\pi nMT}{c\rho V}=\frac{2\pi nM}{c\rho K},$

$t_2=t_1+\frac{2\pi nM}{c\rho K}=20+\frac{2\cdot 3.14\cdot 16.67\cdot 10000}{4200\cdot 1000\cdot 0.5}=20.5~°C.$