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A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.?
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A pelton wheel is working under a head of 45 m and the discharge is 0....
Solution:
Given data:
Head (H) = 45 m
Discharge (Q) = 0.8 m^3/s
Mean bucket speed (V) = 14 m/s
Deflection angle (θ) = 165°
Coefficient of velocity (Cv) = 0.985
Mechanical efficiency (ηm) = 0.95
Bucket friction coefficient (μ) = 0.96
To find:
Overall efficiency (ηo) and shaft power produced (P)
Calculation of velocity of the jet (Vj):
The velocity of the jet can be calculated using the following formula:
Vj = (2gh)^0.5
Where,
g = acceleration due to gravity = 9.81 m/s^2
h = head = 45 m
Vj = (2 x 9.81 x 45)^0.5
Vj = 30.03 m/s
Calculation of actual velocity of the jet (Va):
The actual velocity of the jet can be calculated using the following formula:
Va = Cv x Vj
Va = 0.985 x 30.03
Va = 29.56 m/s
Calculation of effective velocity of the jet (Ve):
The effective velocity of the jet can be calculated using the following formula:
Ve = Va x sin(θ/2)
Ve = 29.56 x sin(165/2)
Ve = 14.15 m/s
Calculation of bucket speed ratio (u):
The bucket speed ratio can be calculated using the following formula:
u = V/Ve
u = 14/14.15
u = 0.991
Calculation of power produced (P):
The power produced can be calculated using the following formula:
P = ρQgHηmηo
Where,
ρ = density of water = 1000 kg/m^3
g = acceleration due to gravity = 9.81 m/s^2
Q = discharge = 0.8 m^3/s
H = head = 45 m
ηm = mechanical efficiency = 0.95
ηo = overall efficiency
μ = bucket friction coefficient = 0.96
Assuming the losses due to friction and other losses are negligible, the overall efficiency can be calculated as:
ηo = u x ηb
Where,
ηb = bucket efficiency
The bucket efficiency can be calculated using the following formula:
ηb = 1 - (1 - μ) x (V/Ve)^2
ηb = 1 - (1 - 0.96) x (14/14.15)^2
ηb = 0.924
ηo = 0.991 x 0.924
ηo = 0.916
P = 1000 x 0.8 x 9.81 x 45 x 0.95 x 0.916
P = 281.12 kW
Therefore, the overall efficiency of the pelton wheel is 0.916 and the shaft power produced is 281.12 kW.
Given data:
Head (H) = 45 m
Discharge (Q) = 0.8 m^3/s
Mean bucket speed (V) = 14 m/s
Deflection angle (θ) = 165°
Coefficient of velocity (Cv) = 0.985
Mechanical efficiency (ηm) = 0.95
Bucket friction coefficient (μ) = 0.96
To find:
Overall efficiency (ηo) and shaft power produced (P)
Calculation of velocity of the jet (Vj):
The velocity of the jet can be calculated using the following formula:
Vj = (2gh)^0.5
Where,
g = acceleration due to gravity = 9.81 m/s^2
h = head = 45 m
Vj = (2 x 9.81 x 45)^0.5
Vj = 30.03 m/s
Calculation of actual velocity of the jet (Va):
The actual velocity of the jet can be calculated using the following formula:
Va = Cv x Vj
Va = 0.985 x 30.03
Va = 29.56 m/s
Calculation of effective velocity of the jet (Ve):
The effective velocity of the jet can be calculated using the following formula:
Ve = Va x sin(θ/2)
Ve = 29.56 x sin(165/2)
Ve = 14.15 m/s
Calculation of bucket speed ratio (u):
The bucket speed ratio can be calculated using the following formula:
u = V/Ve
u = 14/14.15
u = 0.991
Calculation of power produced (P):
The power produced can be calculated using the following formula:
P = ρQgHηmηo
Where,
ρ = density of water = 1000 kg/m^3
g = acceleration due to gravity = 9.81 m/s^2
Q = discharge = 0.8 m^3/s
H = head = 45 m
ηm = mechanical efficiency = 0.95
ηo = overall efficiency
μ = bucket friction coefficient = 0.96
Assuming the losses due to friction and other losses are negligible, the overall efficiency can be calculated as:
ηo = u x ηb
Where,
ηb = bucket efficiency
The bucket efficiency can be calculated using the following formula:
ηb = 1 - (1 - μ) x (V/Ve)^2
ηb = 1 - (1 - 0.96) x (14/14.15)^2
ηb = 0.924
ηo = 0.991 x 0.924
ηo = 0.916
P = 1000 x 0.8 x 9.81 x 45 x 0.95 x 0.916
P = 281.12 kW
Therefore, the overall efficiency of the pelton wheel is 0.916 and the shaft power produced is 281.12 kW.
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A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.?
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A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.? 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 A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.?.
A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.? 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 A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.?.
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A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.?, a detailed solution for A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.? has been provided alongside types of A pelton wheel is working under a head of 45 m and the discharge is 0.8 m^3/s.The mean bucket speed is 14m/s. Find the overall efficiency and shaft power produced if the jet is deflected by the bucket through an angle of 165.assume coefficient of velocity = 0.985 and mechanical efficiency 0.95. The bucket friction coefficient can be assumed as 0.96.? theory, EduRev gives you an
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