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Two small circular orifice of diameters d1 and d2, respectively, are placed on the side of a tank at depths of 25 cm and 1 m below a consistently maintained surface of water. If the discharges through the orifices are the same, what is the ratio of the diameter d1 to d2
- a)1/2
- b)1/√2
- c)2
- d)√2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two small circular orifice of diameters d1and d2, respectively, are pl...
The discharge through an orifice is given by the formula $Q = CdA\sqrt{2gh}$, where $Q$ is the discharge rate, $C$ is the coefficient of discharge (which we assume is the same for both orifices), $d$ is the diameter of the orifice, $A$ is the area of the orifice, $g$ is the acceleration due to gravity, and $h$ is the depth of the orifice below the surface of the water.
Since the discharges through the orifices are the same, we have:
$$Cd_1A_1\sqrt{2gh_1} = Cd_2A_2\sqrt{2gh_2}$$
Dividing both sides by $Cd_1A_1\sqrt{2g}$, we get:
$$\sqrt{\frac{h_1}{d_1}} = \sqrt{\frac{h_2}{d_2}}$$
Squaring both sides, we get:
$$\frac{h_1}{d_1} = \frac{h_2}{d_2}$$
Since $h_1 = 25\text{ cm}$ and $h_2 = 1\text{ m} = 100\text{ cm}$, we have:
$$\frac{25}{d_1} = \frac{100}{d_2}$$
Simplifying, we get:
$$d_2 = 4d_1$$
Therefore, the ratio of $d_1$ to $d_2$ is:
$$\frac{d_1}{d_2} = \frac{1}{4}$$
So the answer is $\boxed{\textbf{(a) }1/2}$.
Since the discharges through the orifices are the same, we have:
$$Cd_1A_1\sqrt{2gh_1} = Cd_2A_2\sqrt{2gh_2}$$
Dividing both sides by $Cd_1A_1\sqrt{2g}$, we get:
$$\sqrt{\frac{h_1}{d_1}} = \sqrt{\frac{h_2}{d_2}}$$
Squaring both sides, we get:
$$\frac{h_1}{d_1} = \frac{h_2}{d_2}$$
Since $h_1 = 25\text{ cm}$ and $h_2 = 1\text{ m} = 100\text{ cm}$, we have:
$$\frac{25}{d_1} = \frac{100}{d_2}$$
Simplifying, we get:
$$d_2 = 4d_1$$
Therefore, the ratio of $d_1$ to $d_2$ is:
$$\frac{d_1}{d_2} = \frac{1}{4}$$
So the answer is $\boxed{\textbf{(a) }1/2}$.
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Community Answer
Two small circular orifice of diameters d1and d2, respectively, are pl...
Concept:
Discharge through a circular orifice is given by;
Where, a = Area of orifice
h = Head above the surface
Calculation:
Given,
Discharge through the orifices are same
h1 = 25 cm, h2 = 1 m = 100 cm
∵ we know that,
and, Q1 = Q2
Discharge through a circular orifice is given by;
Where, a = Area of orifice
h = Head above the surface
Calculation:
Given,
Discharge through the orifices are same
h1 = 25 cm, h2 = 1 m = 100 cm
∵ we know that,
and, Q1 = Q2
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Two small circular orifice of diameters d1and d2, respectively, are placed on the side of a tank at depths of 25 cm and 1 m below a consistently maintained surface of water. If the discharges through the orifices are the same, what is the ratio of the diameter d1to d2a)1/2b)1/√2c)2d)√2Correct answer is option 'D'. Can you explain this answer?
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Two small circular orifice of diameters d1and d2, respectively, are placed on the side of a tank at depths of 25 cm and 1 m below a consistently maintained surface of water. If the discharges through the orifices are the same, what is the ratio of the diameter d1to d2a)1/2b)1/√2c)2d)√2Correct answer is option 'D'. Can you explain this answer? 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 Two small circular orifice of diameters d1and d2, respectively, are placed on the side of a tank at depths of 25 cm and 1 m below a consistently maintained surface of water. If the discharges through the orifices are the same, what is the ratio of the diameter d1to d2a)1/2b)1/√2c)2d)√2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two small circular orifice of diameters d1and d2, respectively, are placed on the side of a tank at depths of 25 cm and 1 m below a consistently maintained surface of water. If the discharges through the orifices are the same, what is the ratio of the diameter d1to d2a)1/2b)1/√2c)2d)√2Correct answer is option 'D'. Can you explain this answer?.
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