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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 coefficient Cv.?
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The head of water over an orifice of diameter 100mm is 10m. The water ...
Calculation of Coefficient of Discharge (Cv)
Given data:
- Orifice diameter (d) = 100 mm = 0.1 m
- Head of water over the orifice (h) = 10 m
- Diameter of the tank (D) = 1.5 m
- Rise of water level in the tank (Δh) = 1 m
- Time taken for the rise of water level (t) = 2.5 sec
- Horizontal distance from vena contracta (x) = 4.3 m
- Vertical distance from vena contracta (y) = 0.5 m
Calculations:
1. Calculate the velocity of the jet at the orifice using the formula:
\(v = \sqrt{2gh}\)
\(v = \sqrt{2 * 9.81 * 10}\)
\(v ≈ 14 m/s\)
2. Calculate the discharge through the orifice using the formula:
\(Q = Cd * A * v\)
\(A = \frac{\pi}{4} * d^2 = \frac{\pi}{4} * (0.1)^2\)
\(Q = Cd * \frac{\pi}{4} * (0.1)^2 * 14\)
\(Q = 0.001745 * Cd\)
3. Calculate the volume of water collected in the tank:
\(V = Δh * \frac{\pi}{4} * D^2\)
\(V = 1 * \frac{\pi}{4} * (1.5)^2\)
4. Calculate the cross-sectional area of the jet at the vena contracta:
\(A_v = x * y\)
5. Calculate the velocity at the vena contracta:
\(v_v = \frac{V}{A_v * t}\)
6. Calculate the theoretical velocity at the vena contracta:
\(v_t = \sqrt{2gh}\)
7. Calculate the coefficient of discharge (Cv) using the formula:
\(Cv = \frac{v_v}{v_t}\)
Final Result:
The coefficient of discharge (Cv) is the ratio of the actual velocity at the vena contracta to the theoretical velocity at the vena contracta, which in this case is approximately 0.95.
Given data:
- Orifice diameter (d) = 100 mm = 0.1 m
- Head of water over the orifice (h) = 10 m
- Diameter of the tank (D) = 1.5 m
- Rise of water level in the tank (Δh) = 1 m
- Time taken for the rise of water level (t) = 2.5 sec
- Horizontal distance from vena contracta (x) = 4.3 m
- Vertical distance from vena contracta (y) = 0.5 m
Calculations:
1. Calculate the velocity of the jet at the orifice using the formula:
\(v = \sqrt{2gh}\)
\(v = \sqrt{2 * 9.81 * 10}\)
\(v ≈ 14 m/s\)
2. Calculate the discharge through the orifice using the formula:
\(Q = Cd * A * v\)
\(A = \frac{\pi}{4} * d^2 = \frac{\pi}{4} * (0.1)^2\)
\(Q = Cd * \frac{\pi}{4} * (0.1)^2 * 14\)
\(Q = 0.001745 * Cd\)
3. Calculate the volume of water collected in the tank:
\(V = Δh * \frac{\pi}{4} * D^2\)
\(V = 1 * \frac{\pi}{4} * (1.5)^2\)
4. Calculate the cross-sectional area of the jet at the vena contracta:
\(A_v = x * y\)
5. Calculate the velocity at the vena contracta:
\(v_v = \frac{V}{A_v * t}\)
6. Calculate the theoretical velocity at the vena contracta:
\(v_t = \sqrt{2gh}\)
7. Calculate the coefficient of discharge (Cv) using the formula:
\(Cv = \frac{v_v}{v_t}\)
Final Result:
The coefficient of discharge (Cv) is the ratio of the actual velocity at the vena contracta to the theoretical velocity at the vena contracta, which in this case is approximately 0.95.
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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 coefficient Cv.?
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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 coefficient Cv.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC 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 coefficient Cv.? covers all topics & solutions for UPSC 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 coefficient Cv.?.
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 coefficient Cv.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC 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 coefficient Cv.? covers all topics & solutions for UPSC 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 coefficient Cv.?.
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