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The head of water over an orifice of diameter 100mm is 10m. The water coming out from orifice is collected in a circular tank of diameter 1.5m. The rise of water level in this tank is 1m in 2.5sec. Also the coordinates of a point on the jet measured from vena-contracta are 4.3m horizontal and 0.5m vertical. Find the coefficients Cd, Cv and Cc?
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The head of water over an orifice of diameter 100mm is 10m. The water ...
Solution:
Given data:
Diameter of orifice (D) = 100mm
Head of water over the orifice (H) = 10m
Diameter of the circular tank (d) = 1.5m
Rise in water level in tank (h) = 1m
Time taken for rise in water level (t) = 2.5sec
Horizontal distance of point from vena-contracta (x) = 4.3m
Vertical distance of point from vena-contracta (y) = 0.5m
We need to find the coefficients Cd, Cv, and Cc.
Calculation of Coefficient of Discharge (Cd):
The coefficient of discharge is defined as the ratio of actual discharge to theoretical discharge. Theoretical discharge is given by the formula:
Q = Cd * A * √(2gH)
Where,
Q = Theoretical discharge
A = Area of orifice
g = Acceleration due to gravity
Area of orifice can be calculated using the formula:
A = π/4 * D^2
Substituting the values, we get:
A = π/4 * (0.1m)^2 = 0.00785 m^2
g = 9.81 m/s^2
Substituting the values in the formula for Q, we get:
Q = Cd * 0.00785 * √(2 * 9.81 * 10)
Q = 0.443 Cd
Actual discharge can be calculated using the formula:
Q = Av
Where,
A = Area of jet at vena-contracta
v = Velocity of jet at vena-contracta
Area of jet at vena-contracta can be calculated using the formula:
A = π/4 * d^2
Substituting the values, we get:
A = π/4 * (1.5m)^2 = 1.7671 m^2
Velocity of jet at vena-contracta can be calculated using the formula:
v = √(2gH)
Substituting the values, we get:
v = √(2 * 9.81 * 10) = 14.01 m/s
Substituting the values in the formula for actual discharge, we get:
Q = 1.7671 * 14.01 = 24.744 m^3/s
Substituting the values of theoretical and actual discharge, we get:
0.443 Cd = 24.744
Cd = 55.83
Therefore, the coefficient of discharge (Cd) is 55.83.
Calculation of Coefficient of Velocity (Cv):
The coefficient of velocity is defined as the ratio of actual velocity to theoretical velocity. Theoretical velocity is given by the formula:
V = √(2gH)
Where,
V = Theoretical velocity
Substituting the values, we get:
V = √(2 * 9.81 * 10) = 14.01 m/s
Actual velocity can be calculated using the formula:
v = √(x^2 + y^2)/t
Substituting the values, we get:
v = √(4.3^2 + 0.5^2)/2.5 = 2.074 m/s
Given data:
Diameter of orifice (D) = 100mm
Head of water over the orifice (H) = 10m
Diameter of the circular tank (d) = 1.5m
Rise in water level in tank (h) = 1m
Time taken for rise in water level (t) = 2.5sec
Horizontal distance of point from vena-contracta (x) = 4.3m
Vertical distance of point from vena-contracta (y) = 0.5m
We need to find the coefficients Cd, Cv, and Cc.
Calculation of Coefficient of Discharge (Cd):
The coefficient of discharge is defined as the ratio of actual discharge to theoretical discharge. Theoretical discharge is given by the formula:
Q = Cd * A * √(2gH)
Where,
Q = Theoretical discharge
A = Area of orifice
g = Acceleration due to gravity
Area of orifice can be calculated using the formula:
A = π/4 * D^2
Substituting the values, we get:
A = π/4 * (0.1m)^2 = 0.00785 m^2
g = 9.81 m/s^2
Substituting the values in the formula for Q, we get:
Q = Cd * 0.00785 * √(2 * 9.81 * 10)
Q = 0.443 Cd
Actual discharge can be calculated using the formula:
Q = Av
Where,
A = Area of jet at vena-contracta
v = Velocity of jet at vena-contracta
Area of jet at vena-contracta can be calculated using the formula:
A = π/4 * d^2
Substituting the values, we get:
A = π/4 * (1.5m)^2 = 1.7671 m^2
Velocity of jet at vena-contracta can be calculated using the formula:
v = √(2gH)
Substituting the values, we get:
v = √(2 * 9.81 * 10) = 14.01 m/s
Substituting the values in the formula for actual discharge, we get:
Q = 1.7671 * 14.01 = 24.744 m^3/s
Substituting the values of theoretical and actual discharge, we get:
0.443 Cd = 24.744
Cd = 55.83
Therefore, the coefficient of discharge (Cd) is 55.83.
Calculation of Coefficient of Velocity (Cv):
The coefficient of velocity is defined as the ratio of actual velocity to theoretical velocity. Theoretical velocity is given by the formula:
V = √(2gH)
Where,
V = Theoretical velocity
Substituting the values, we get:
V = √(2 * 9.81 * 10) = 14.01 m/s
Actual velocity can be calculated using the formula:
v = √(x^2 + y^2)/t
Substituting the values, we get:
v = √(4.3^2 + 0.5^2)/2.5 = 2.074 m/s
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The head of water over an orifice of diameter 100mm is 10m. The water coming out from orifice is collected in a circular tank of diameter 1.5m. The rise of water level in this tank is 1m in 2.5sec. Also the coordinates of a point on the jet measured from vena-contracta are 4.3m horizontal and 0.5m vertical. Find the coefficients Cd, Cv and Cc?
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The head of water over an orifice of diameter 100mm is 10m. The water coming out from orifice is collected in a circular tank of diameter 1.5m. The rise of water level in this tank is 1m in 2.5sec. Also the coordinates of a point on the jet measured from vena-contracta are 4.3m horizontal and 0.5m vertical. Find the coefficients Cd, Cv and Cc? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The head of water over an orifice of diameter 100mm is 10m. The water coming out from orifice is collected in a circular tank of diameter 1.5m. The rise of water level in this tank is 1m in 2.5sec. Also the coordinates of a point on the jet measured from vena-contracta are 4.3m horizontal and 0.5m vertical. Find the coefficients Cd, Cv and Cc? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The head of water over an orifice of diameter 100mm is 10m. The water coming out from orifice is collected in a circular tank of diameter 1.5m. The rise of water level in this tank is 1m in 2.5sec. Also the coordinates of a point on the jet measured from vena-contracta are 4.3m horizontal and 0.5m vertical. Find the coefficients Cd, Cv and Cc?.
The head of water over an orifice of diameter 100mm is 10m. The water coming out from orifice is collected in a circular tank of diameter 1.5m. The rise of water level in this tank is 1m in 2.5sec. Also the coordinates of a point on the jet measured from vena-contracta are 4.3m horizontal and 0.5m vertical. Find the coefficients Cd, Cv and Cc? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The head of water over an orifice of diameter 100mm is 10m. The water coming out from orifice is collected in a circular tank of diameter 1.5m. The rise of water level in this tank is 1m in 2.5sec. Also the coordinates of a point on the jet measured from vena-contracta are 4.3m horizontal and 0.5m vertical. Find the coefficients Cd, Cv and Cc? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The head of water over an orifice of diameter 100mm is 10m. The water coming out from orifice is collected in a circular tank of diameter 1.5m. The rise of water level in this tank is 1m in 2.5sec. Also the coordinates of a point on the jet measured from vena-contracta are 4.3m horizontal and 0.5m vertical. Find the coefficients Cd, Cv and Cc?.
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