We were discussing a new topic, in the subject of fluid mechanics and hydraulics machine, i.e. an introduction to hydraulic machine and various types of hydraulic turbines in our recent posts.Â

Now we will focus here to understand some important terminologies associated with a hydraulic turbine such as Gross head, Net head and efficiencies of a hydraulic turbine with the help of this post.Â

Will you be interested today to find out these important terminologies associated with a hydraulic turbine?Â

So let us start here with the following important terminologiesÂ

Gross head is basically defined as the difference between the head race level and tail race level when water is not flowing. Gross head will be indicated by Hg as displayed here in following figure.Â

Net head is basically defined as the head available at the inlet of the turbine. Net head is also simply called as effective head.Â

When water will flow from head race to the turbine, there will be some losses of head due to friction between water and penstock. There will also be other losses of head such as loss of head due to bend, fitting, at entrance of penstock etc. We must note it here that these losses will be very less and could be neglected when we compare with head loss due to friction.Â

Net head available at the inlet of turbine could be written as mentioned here.Â

Loss of head due to friction will be given by Darcy-Weisbach equation and we can find it here.Â

Efficiencies of a turbineÂ

There are following important efficiencies that we will discuss here in this post.
1. Hydraulic efficiency
2. Mechanical Efficiency
3. Volumetric efficiency
4. Overall EfficiencyÂ

Hydraulic efficiencyÂ

Hydraulic efficiency is basically defined as the ratio of power given by water to the runner of turbine to the power supplied by the water at the inlet of the turbine. Hydraulic efficiency will be indicated by Î·h.Â

Runner is basically a rotating component of a turbine and buckets or vanes will be fixed at the circumference of the runner.Â

Vanes or buckets fixed on the runner are not smooth and hence there will be hydraulic losses when water will flow through these vanes of the turbine. Therefore, power given by water to the runner of the turbine will be less than the power supplied by the water at the inlet of the turbine.Â

Hydraulic efficiency of a turbine could be written as mentioned here

Hydraulic efficiency (Î·h) = Power delivered to the runner of turbine / Power supplied at the inlet of turbine Â Hydraulic efficiency (Î·h) = R.P/ W.P

R.P = Power delivered to the runner of turbine
W.P = Power supplied at the inlet of turbine or water powerÂ

Mechanical EfficiencyÂ

Mechanical efficiency is basically defined as the ratio of power available at the shaft of the turbine to the power delivered to the runner of the turbine. Mechanical efficiency will be indicated by Î·m.Â Â

Power given by water to the runner of turbine will be transmitted to the shaft of the turbine. Power available at the shaft of the turbine will be less than the power delivered to the runner of the turbine due to mechanical losses.Â

Mechanical efficiency of a turbine could be written as mentioned here

Mechanical efficiency (Î·m) = Power available at the shaft of the turbine / Power delivered to the runner of the turbine Mechanical efficiency (Î·m) = S.P/ R.P

S.P = Power available at the shaft of the turbine
R.P = Power delivered to the runner of turbineÂ

Volumetric EfficiencyÂ

The volume of the water striking the runner of a turbine will be slightly less than the volume of the water supplied to the turbine as some amount of water will be discharged to the tail race without striking the runner of the turbine.Â

Volumetric efficiency is basically defined as the ratio of the volume of the water actually striking the runner of the turbine to the volume of water supplied to the turbine. Volumetric efficiency will be indicated by Î·v.Â

Volumetric efficiency of a turbine could be written as mentioned here Â

Overall EfficiencyÂ

Overall efficiency is basically defined as the ratio of the power available at the shaft of the turbine to the power supplied by the water at the inlet of the turbine. Overall efficiency will be indicated by Î·o. Â

Overall efficiency, Î·o = Power available at the shaft of the turbine / Power supplied by the water at the inlet of the turbine Overall efficiency, Î·o = S.P/W.P

Overall efficiency is also defined as the product of mechanical efficiency and hydraulic efficiency

Overall efficiency = Mechanical efficiency x Hydraulic efficiency Î·o = Î·m x Î·h

You should also find out the following important posts those are very useful and must need to read.Â

Do you have any suggestions? Please write in comment box.Â

Further we will find out, in our next post,Â

Reference:Â

Fluid mechanics, By R. K. BansalÂ