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A rectangular orifice of 2 m width and 1.2 m deep is fitted in one side of large tank. The easier level on one side of the orifice is 3m above the top edge of the orifice while on the other side of the orifice the water level is 0.5 m below it’s top edge. Calculate discharge if Cd = .64
- a)4.95 m3/s
- b)5.67 m3/s
- c)3.56 m3/s
- d)6.75 m3/s
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A rectangular orifice of 2 m width and 1.2 m deep is fitted in one sid...
Explanation: Explanation: Q = Cd * b * (H2 – H) √2gH
Here, b = 2
H2 = 4.2
Here, b = 2
H2 = 4.2
H = 3.5
Q = 4.94 m3/s.
Q = 4.94 m3/s.
Most Upvoted Answer
A rectangular orifice of 2 m width and 1.2 m deep is fitted in one sid...
To solve this problem, we can use Bernoulli's equation which states that the total energy of a fluid is conserved along a streamline. This equation can be written as:
P1 + 0.5ρv1^2 + ρgh1 = P2 + 0.5ρv2^2 + ρgh2
where P is the pressure, ρ is the density, v is the velocity, h is the height above a reference point, and subscripts 1 and 2 refer to two different points in the flow.
In this case, we can assume that the flow is steady and incompressible, so the mass flow rate through the orifice is constant. We can also neglect frictional losses and assume that the flow is horizontal. With these assumptions, we can write the equation for the two points as:
P1 + ρgh1 = P2 + ρgh2
where P1 and P2 are the pressures on either side of the orifice, and h1 and h2 are the heights of the water levels above a reference point.
We can choose the reference point to be the top edge of the orifice, so h1 = 3 m and h2 = -0.5 m (since the water level is below the orifice on the other side). We also know that the width of the orifice is 2 m and the depth is 1.2 m. Therefore, the area of the orifice is:
A = width x depth = 2 x 1.2 = 2.4 m^2
The mass flow rate through the orifice can be calculated using the equation:
Q = A x v
where Q is the mass flow rate and v is the velocity of the water through the orifice. Since the density of water is approximately 1000 kg/m^3, we can write:
Q = A x v x ρ = 2.4 x v x 1000
Now we can use the Bernoulli's equation to solve for the velocity v:
P1 + ρgh1 = P2 + ρgh2
We can assume that the pressure on both sides of the orifice is atmospheric pressure (101325 Pa), so we can simplify the equation to:
ρgh1 = ρgh2
3 x 1000 x 9.81 = (-0.5) x 1000 x 9.81 + 0.5ρv^2
29430 = 490.5 + 0.5ρv^2
ρv^2 = 58860
v^2 = 58.86
v = 7.67 m/s (approximately)
Therefore, the mass flow rate through the orifice is:
Q = 2.4 x v x 1000 = 18408 kg/h (approximately)
P1 + 0.5ρv1^2 + ρgh1 = P2 + 0.5ρv2^2 + ρgh2
where P is the pressure, ρ is the density, v is the velocity, h is the height above a reference point, and subscripts 1 and 2 refer to two different points in the flow.
In this case, we can assume that the flow is steady and incompressible, so the mass flow rate through the orifice is constant. We can also neglect frictional losses and assume that the flow is horizontal. With these assumptions, we can write the equation for the two points as:
P1 + ρgh1 = P2 + ρgh2
where P1 and P2 are the pressures on either side of the orifice, and h1 and h2 are the heights of the water levels above a reference point.
We can choose the reference point to be the top edge of the orifice, so h1 = 3 m and h2 = -0.5 m (since the water level is below the orifice on the other side). We also know that the width of the orifice is 2 m and the depth is 1.2 m. Therefore, the area of the orifice is:
A = width x depth = 2 x 1.2 = 2.4 m^2
The mass flow rate through the orifice can be calculated using the equation:
Q = A x v
where Q is the mass flow rate and v is the velocity of the water through the orifice. Since the density of water is approximately 1000 kg/m^3, we can write:
Q = A x v x ρ = 2.4 x v x 1000
Now we can use the Bernoulli's equation to solve for the velocity v:
P1 + ρgh1 = P2 + ρgh2
We can assume that the pressure on both sides of the orifice is atmospheric pressure (101325 Pa), so we can simplify the equation to:
ρgh1 = ρgh2
3 x 1000 x 9.81 = (-0.5) x 1000 x 9.81 + 0.5ρv^2
29430 = 490.5 + 0.5ρv^2
ρv^2 = 58860
v^2 = 58.86
v = 7.67 m/s (approximately)
Therefore, the mass flow rate through the orifice is:
Q = 2.4 x v x 1000 = 18408 kg/h (approximately)
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A rectangular orifice of 2 m width and 1.2 m deep is fitted in one side of large tank. The easier level on one side of the orifice is 3m above the top edge of the orifice while on the other side of the orifice the water level is 0.5 m below it’s top edge. Calculate discharge if Cd = .64a)4.95 m3/sb)5.67 m3/sc)3.56 m3/sd)6.75 m3/sCorrect answer is option 'A'. Can you explain this answer?
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A rectangular orifice of 2 m width and 1.2 m deep is fitted in one side of large tank. The easier level on one side of the orifice is 3m above the top edge of the orifice while on the other side of the orifice the water level is 0.5 m below it’s top edge. Calculate discharge if Cd = .64a)4.95 m3/sb)5.67 m3/sc)3.56 m3/sd)6.75 m3/sCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A rectangular orifice of 2 m width and 1.2 m deep is fitted in one side of large tank. The easier level on one side of the orifice is 3m above the top edge of the orifice while on the other side of the orifice the water level is 0.5 m below it’s top edge. Calculate discharge if Cd = .64a)4.95 m3/sb)5.67 m3/sc)3.56 m3/sd)6.75 m3/sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular orifice of 2 m width and 1.2 m deep is fitted in one side of large tank. The easier level on one side of the orifice is 3m above the top edge of the orifice while on the other side of the orifice the water level is 0.5 m below it’s top edge. Calculate discharge if Cd = .64a)4.95 m3/sb)5.67 m3/sc)3.56 m3/sd)6.75 m3/sCorrect answer is option 'A'. Can you explain this answer?.
A rectangular orifice of 2 m width and 1.2 m deep is fitted in one side of large tank. The easier level on one side of the orifice is 3m above the top edge of the orifice while on the other side of the orifice the water level is 0.5 m below it’s top edge. Calculate discharge if Cd = .64a)4.95 m3/sb)5.67 m3/sc)3.56 m3/sd)6.75 m3/sCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A rectangular orifice of 2 m width and 1.2 m deep is fitted in one side of large tank. The easier level on one side of the orifice is 3m above the top edge of the orifice while on the other side of the orifice the water level is 0.5 m below it’s top edge. Calculate discharge if Cd = .64a)4.95 m3/sb)5.67 m3/sc)3.56 m3/sd)6.75 m3/sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular orifice of 2 m width and 1.2 m deep is fitted in one side of large tank. The easier level on one side of the orifice is 3m above the top edge of the orifice while on the other side of the orifice the water level is 0.5 m below it’s top edge. Calculate discharge if Cd = .64a)4.95 m3/sb)5.67 m3/sc)3.56 m3/sd)6.75 m3/sCorrect answer is option 'A'. Can you explain this answer?.
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