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For a Kaplan turbine with a runner diameter 4meter the discharge is 60 cubic
meters/sec and the hydraulic and mechanical efficiencies 90% and 94% resp. The
diameter of boss is 0.3 times the runner diameter and speed ratio is 2.0. Assuming that
discharge is free and there is no whirl at outlet, calculate the net available head on the
turbine and specific speed.?
meters/sec and the hydraulic and mechanical efficiencies 90% and 94% resp. The
diameter of boss is 0.3 times the runner diameter and speed ratio is 2.0. Assuming that
discharge is free and there is no whirl at outlet, calculate the net available head on the
turbine and specific speed.?
Most Upvoted Answer
For a Kaplan turbine with a runner diameter 4meter the discharge is 60...
Calculation of Net Available Head and Specific Speed for a Kaplan Turbine
Net Available Head Calculation:
The net available head (H) is the difference between the total head (Ht) and the head losses (hL) in the turbine. The total head can be calculated using the following formula:
Ht = (Q^2/2g) + Hf + Hs + Hb
Where Q is the discharge, g is the acceleration due to gravity, Hf is the head loss due to friction, Hs is the head loss due to sudden contraction or expansion, and Hb is the head loss due to the presence of the boss.
Assuming that there is no head loss due to friction, sudden contraction or expansion, and the discharge is free, the total head reduces to:
Ht = (Q^2/2g) + Hb
The hydraulic efficiency (ηh) is given as 90% or 0.9, and the mechanical efficiency (ηm) is given as 94% or 0.94. The overall efficiency (η) is given by:
η = ηh x ηm
η = 0.9 x 0.94
η = 0.846 or 84.6%
The net available head can be calculated using the following formula:
H = (Ht x η)/s
Where s is the speed ratio.
Substituting the given values:
Q = 60 m^3/s
D = 4 m
d = 0.3D = 1.2 m
s = 2.0
g = 9.81 m/s^2
η = 0.846
Ht = (Q^2/2g) + Hb
Ht = ((60^2)/(2 x 9.81)) + 0
Ht = 1819.8 m
H = (Ht x η)/s
H = (1819.8 x 0.846)/2.0
H = 770.1 m
Therefore, the net available head on the turbine is 770.1 m.
Specific Speed Calculation:
The specific speed (Ns) of a turbine is a dimensionless quantity that describes the speed at which a turbine would run if it were geometrically similar and had a unit head and a unit discharge. It is given by the following formula:
Ns = (n√Q)/H^0.75
Where n is the speed of the turbine in rpm, Q is the discharge in m^3/s, and H is the net available head in m.
Substituting the given values:
Q = 60 m^3/s
D = 4 m
d = 0.3D = 1.2 m
s = 2.0
g = 9.81 m/s^2
η = 0.846
H = 770.1 m
The speed of the turbine (n) can be calculated using the following formula:
n = (60 x s x D)/πd
n = (60 x 2.0 x 4)/π x 1.2
n = 314.2 rpm
Ns = (n√Q)/H^0.75
Ns = (314.2 x √60)/770.1^0
Net Available Head Calculation:
The net available head (H) is the difference between the total head (Ht) and the head losses (hL) in the turbine. The total head can be calculated using the following formula:
Ht = (Q^2/2g) + Hf + Hs + Hb
Where Q is the discharge, g is the acceleration due to gravity, Hf is the head loss due to friction, Hs is the head loss due to sudden contraction or expansion, and Hb is the head loss due to the presence of the boss.
Assuming that there is no head loss due to friction, sudden contraction or expansion, and the discharge is free, the total head reduces to:
Ht = (Q^2/2g) + Hb
The hydraulic efficiency (ηh) is given as 90% or 0.9, and the mechanical efficiency (ηm) is given as 94% or 0.94. The overall efficiency (η) is given by:
η = ηh x ηm
η = 0.9 x 0.94
η = 0.846 or 84.6%
The net available head can be calculated using the following formula:
H = (Ht x η)/s
Where s is the speed ratio.
Substituting the given values:
Q = 60 m^3/s
D = 4 m
d = 0.3D = 1.2 m
s = 2.0
g = 9.81 m/s^2
η = 0.846
Ht = (Q^2/2g) + Hb
Ht = ((60^2)/(2 x 9.81)) + 0
Ht = 1819.8 m
H = (Ht x η)/s
H = (1819.8 x 0.846)/2.0
H = 770.1 m
Therefore, the net available head on the turbine is 770.1 m.
Specific Speed Calculation:
The specific speed (Ns) of a turbine is a dimensionless quantity that describes the speed at which a turbine would run if it were geometrically similar and had a unit head and a unit discharge. It is given by the following formula:
Ns = (n√Q)/H^0.75
Where n is the speed of the turbine in rpm, Q is the discharge in m^3/s, and H is the net available head in m.
Substituting the given values:
Q = 60 m^3/s
D = 4 m
d = 0.3D = 1.2 m
s = 2.0
g = 9.81 m/s^2
η = 0.846
H = 770.1 m
The speed of the turbine (n) can be calculated using the following formula:
n = (60 x s x D)/πd
n = (60 x 2.0 x 4)/π x 1.2
n = 314.2 rpm
Ns = (n√Q)/H^0.75
Ns = (314.2 x √60)/770.1^0
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For a Kaplan turbine with a runner diameter 4meter the discharge is 60 cubicmeters/sec and the hydraulic and mechanical efficiencies 90% and 94% resp. Thediameter of boss is 0.3 times the runner diameter and speed ratio is 2.0. Assuming thatdischarge is free and there is no whirl at outlet, calculate the net available head on theturbine and specific speed.?
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For a Kaplan turbine with a runner diameter 4meter the discharge is 60 cubicmeters/sec and the hydraulic and mechanical efficiencies 90% and 94% resp. Thediameter of boss is 0.3 times the runner diameter and speed ratio is 2.0. Assuming thatdischarge is free and there is no whirl at outlet, calculate the net available head on theturbine and specific speed.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about For a Kaplan turbine with a runner diameter 4meter the discharge is 60 cubicmeters/sec and the hydraulic and mechanical efficiencies 90% and 94% resp. Thediameter of boss is 0.3 times the runner diameter and speed ratio is 2.0. Assuming thatdischarge is free and there is no whirl at outlet, calculate the net available head on theturbine and specific speed.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a Kaplan turbine with a runner diameter 4meter the discharge is 60 cubicmeters/sec and the hydraulic and mechanical efficiencies 90% and 94% resp. Thediameter of boss is 0.3 times the runner diameter and speed ratio is 2.0. Assuming thatdischarge is free and there is no whirl at outlet, calculate the net available head on theturbine and specific speed.?.
For a Kaplan turbine with a runner diameter 4meter the discharge is 60 cubicmeters/sec and the hydraulic and mechanical efficiencies 90% and 94% resp. Thediameter of boss is 0.3 times the runner diameter and speed ratio is 2.0. Assuming thatdischarge is free and there is no whirl at outlet, calculate the net available head on theturbine and specific speed.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about For a Kaplan turbine with a runner diameter 4meter the discharge is 60 cubicmeters/sec and the hydraulic and mechanical efficiencies 90% and 94% resp. Thediameter of boss is 0.3 times the runner diameter and speed ratio is 2.0. Assuming thatdischarge is free and there is no whirl at outlet, calculate the net available head on theturbine and specific speed.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a Kaplan turbine with a runner diameter 4meter the discharge is 60 cubicmeters/sec and the hydraulic and mechanical efficiencies 90% and 94% resp. Thediameter of boss is 0.3 times the runner diameter and speed ratio is 2.0. Assuming thatdischarge is free and there is no whirl at outlet, calculate the net available head on theturbine and specific speed.?.
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