Lately I did Francis Turbine Experiment at my institute. The objective was to find the efficiency of the turbine. Power input was found using flow rate and pressure gauge. Power output was found by using two spring balances. The spring balances were connected via a belt and wrapped around the shaft. To find the torque difference in forces on spring balances is multiplied by the radius of the shaft. For better understanding you can watch this video https://www.youtube.com/watch?v=3Is-PUC4k1o (ignore the title). I understand why they are being used but did not get the principle behind their usage. How these balances can help to find the torque. Also, when I did this experiment I saw that as net force (Resultant of Left and Right Balance) increases shaft rotational speed decreases: why is this is happening?
The output power $P$ is frictional force $F$ supplied by the belt - which is equal to the difference between the readings of the spring balance - times the speed of the belt over the shaft of the turbine, which is $R\omega$ where $R$ is radius of the shaft and $\omega$ the angular velocity :
This is just an application of the formula power=force$\times$velocity or work=force$\times$distance.
If the input power and efficiency are constant, the output power $P$ of the turbine is constant. An increase in $F$ must cause a decrease in $\omega$. ($R$ is constant.)