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Find the discharge through totally drowned orifice of width 2.3 m if the difference of water levels on both side of the orifice be 40 cm. The height of water from to and bottom of the orifice are 2.6 m and 2.75 m respectively. 
  • a)
    56 m3/s
  • b)
    64 m3/s
  • c)
    75 m3/s
  • d)
    55 m3/s
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Find the discharge through totally drowned orifice of width 2.3 m if t...
Explanation: Q = Cd * b * (H2 – H1) √2gH
Here, b = 2.3
H2 = 2.75
H1 = 2.6
H = 40
Q = .56 m3/s.
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Most Upvoted Answer
Find the discharge through totally drowned orifice of width 2.3 m if t...
To find the discharge through a totally drowned orifice, we can use the formula for the discharge through an orifice:

Q = Cd * A * √(2g * h)

Where:
Q is the discharge
Cd is the discharge coefficient
A is the area of the orifice
g is the acceleration due to gravity
h is the difference in water levels on both sides of the orifice

Let's calculate the values step by step:

1. Finding the area of the orifice (A):
Given the width of the orifice is 2.3 m, and we can assume the height of the orifice to be negligible compared to the width. Therefore, the area of the orifice can be calculated as the product of the width and the height of the orifice:

A = width * height
A = 2.3 m * 0.4 m (40 cm converted to meters)
A = 0.92 m²

2. Finding the difference in water levels (h):
Given the height of water from the top of the orifice is 2.6 m, and from the bottom of the orifice is 2.75 m. The difference in water levels can be calculated by subtracting the height at the bottom from the height at the top:

h = top height - bottom height
h = 2.6 m - 2.75 m
h = -0.15 m

Note: The negative sign indicates that the water level on the bottom side of the orifice is higher than the water level on the top side.

3. Finding the discharge coefficient (Cd):
The discharge coefficient depends on the shape and size of the orifice. For a totally drowned orifice, the discharge coefficient is typically around 0.61.

Cd = 0.61

4. Finding the acceleration due to gravity (g):
The acceleration due to gravity is a constant value of approximately 9.81 m/s².

g = 9.81 m/s²

5. Calculating the discharge (Q):
Now we can substitute the values into the discharge formula:

Q = Cd * A * √(2g * h)
Q = 0.61 * 0.92 m² * √(2 * 9.81 m/s² * -0.15 m)
Q ≈ 56 m³/s

Therefore, the discharge through the totally drowned orifice is approximately 56 m³/s. Hence, the correct answer is option 'A'.
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