# CHARACTERISTIC CURVES OF HYDRAULIC TURBINES

Characteristic curves of a hydraulic turbine are the curves, with the help of which the exact behaviour and performance of the turbine under different working conditions can be known. These curves are plotted from the results of the tests performed on the turbine under different working conditions.

The important parameters which are varied during a test on turbine are:

1) Speed (N)

2) Head (H)

3) Discharge (Q)

4) Power (P)

5) Overall Efficiency

6) Gate opening.

Out of the above six parameters, three parameters namely speed (N), Head (H) and discharge (Q) are **independent parameters**.

Out of the three independent parameters, (N, H, Q) one of the **parameter is kept constant (say H)** and the variation of other two parameters with respect to any one of the remaining two independent variables (say N and Q) are plotted and various curves are obtained. These curves are called characteristic curves. The following are the important characteristic curves of a turbine.

1. Main Characteristic Curves or Constant Head Curves.

2. Operating Characteristic Curves or Constant Speed Curves.

3. Muschel Curves or Constant Efficiency Curves.

## 1. Main Characteristic Curves or Constant Head Curves

These curves are obtained by maintaining a constant head and a constant gate opening (G.O.) on the turbine. The speed of the turbine is varied by changing the load on the turbine. For each value of the speed, the corresponding values of the power (P) and discharge (Q) are obtained. Then the overall efficiency ( ) for each value of the speed is calculated. From

## 2. Operating Characteristic Curves or Constant Speed Curves:

These curves are plotted when the speed on the turbine is constant. In case turbines, the head is generally constant. As already discussed there are three independent parameters namely N, H and Q. For operating characteristics N and H are constant and hence the variation of power and the efficiency with respect to discharge Q are plotted.

The power curve for the turbine shall not pass through the origin, because certain amount of discharge is needed to produce power to overcome initial friction. Hence the power and efficiency curves will be slightly away from the origin on the x-axis, as to overcome initial friction certain amount of discharge will be required.

## 3. Constant Efficiency Curves or Muschel Curves or Iso – Efficiency Curves:

These curves are obtained from the speed vs. efficiency and speed vs. discharge curves for different gate openings. For a given efficiency from the vs. curves there are two speeds. From the vs. curves, corresponding to two values of speeds there are two values of discharge. Hence for a given efficiency there are two values of discharge for a particular gate opening. This means for a given efficiency there are two values of speeds and two values of discharge for a given gate opening. If the efficiency is maximum there is only one value. These two values of speed and two values of discharge. Corresponding to a particular gate opening are plotted.

The procedure is repeated for different gate openings and the curves Q vs. N are plotted. The points having the same efficiencies are joined. The curves having the same efficiency are called Iso-efficiency curves. There curves are helpful for determining the zone of constant efficiency and for predicating the performance of the turbine at various efficiencies.

For plotting the Iso-efficiency curves, horizontal lines representing the same efficiency are drawn on the speed curves. The points at which these lines cut the efficiency curves at various gate opening are transferred to the corresponding speed curves. The points having the same efficiency are then joined by smooth curves. These smooth curves represent the Iso-efficiency curves.