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.

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Net head, H = Gross head (H

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Hydraulic efficiency (Î·

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Volumetric efficiency (Î·

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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.

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

So let us start here with the following important
terminologies

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**Gross
Head **

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 H

_{g}as displayed here in following figure.

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**Net
Head **

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

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.

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

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Net head, H = Gross head (H_{g}) – head loss
due to friction (h_{f})

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

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**Efficiencies
of a turbine **

There are following important efficiencies that we
will discuss here in this post.

- Hydraulic efficiency
- Mechanical Efficiency
- Volumetric efficiency
- Overall Efficiency

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**Hydraulic
efficiency **

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

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.

Hydraulic efficiency of a turbine could be written
as mentioned here

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Hydraulic efficiency (Î·_{h}) = Power
delivered to the runner of turbine / Power supplied at the inlet of turbine 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 power

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**Mechanical
Efficiency **

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}.
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.

Mechanical efficiency of a turbine could be written
as mentioned here

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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

_{m}) = Power available at the shaft of the turbine / Power delivered to the runner of the turbine

_{m}) = S.P/ R.P

S.P = Power available at the shaft of the turbine

R.P = Power delivered to the runner of turbine

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**Volumetric
Efficiency **

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.

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}.
Volumetric efficiency of a turbine could be written
as mentioned here

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Volumetric efficiency (Î·_{v}) = Volume of
the water actually striking the runner of the turbine / Volume of water
supplied to the turbine

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**Overall
Efficiency **

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}.###
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

_{o}= Power available at the shaft of the turbine / Power supplied by the water at the inlet of the turbine

_{o}= S.P/W.P

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

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**Overall
efficiency = Mechanical efficiency x Hydraulic efficiency**
**
****Î·**_{o}
= Î·_{m} x Î·_{h}

**Overall efficiency = Mechanical efficiency x Hydraulic efficiency**

**Î·**

_{o}= Î·_{m}x Î·_{h}
Do you have any suggestions? Please write in comment
box.

Further we will find out, in our next post, Pelton wheel turbine and its components.

### Reference:

Fluid mechanics, By R. K. Bansal

Image courtesy: Google

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