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Two small circular ofifices of diameters d1 and d2 are placed on one side of a tank at depths of 25 cm and 1 m respectively below a constantsurface of water. If the discharges through theorifice are the same, then the ratio of the diameters d1 and d2 will be
- a)1 :2
- b)1: √2
- c)√2 :1
- d)2 : 1
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two small circular ofifices of diameters d1 and d2 are placed on one s...
Solution:
Given,
d1 = diameter of the first orifice = ?
d2 = diameter of the second orifice = ?
h1 = depth of the first orifice = 25 cm = 0.25 m
h2 = depth of the second orifice = 1 m
Let us consider the Bernoulli's equation between section 1 and 2 as shown in the figure below.
Where,
v1 and v2 are the velocities of water at sections 1 and 2 respectively.
p1 and p2 are the pressures at sections 1 and 2 respectively.
z1 and z2 are the elevations of sections 1 and 2 respectively.
hf is the head loss due to friction.
g is the acceleration due to gravity.
As the water level in the tank is constant, the pressure at section 1 and 2 will be atmospheric pressure. Therefore,
p1 = p2 = atmospheric pressure
Also, the head loss due to friction can be neglected as the orifices are small.
Thus, the Bernoulli's equation reduces to:
v1^2/2g + z1 = v2^2/2g + z2
As the discharge through both the orifices is the same, we have:
v1A1 = v2A2
Where,
A1 = cross-sectional area of the first orifice = πd1^2/4
A2 = cross-sectional area of the second orifice = πd2^2/4
Substituting the values of A1 and A2 in the above equation, we get:
v1d1^2 = v2d2^2
Substituting this in the Bernoulli's equation, we get:
d1^2/d2^2 = h2/h1
Substituting the given values, we get:
d1^2/d2^2 = 4
Taking the square root of both sides, we get:
d1/d2 = 2
Therefore, the ratio of the diameters d1 and d2 will be 2:1. Hence, option (C) is the correct answer.
Given,
d1 = diameter of the first orifice = ?
d2 = diameter of the second orifice = ?
h1 = depth of the first orifice = 25 cm = 0.25 m
h2 = depth of the second orifice = 1 m
Let us consider the Bernoulli's equation between section 1 and 2 as shown in the figure below.
Where,
v1 and v2 are the velocities of water at sections 1 and 2 respectively.
p1 and p2 are the pressures at sections 1 and 2 respectively.
z1 and z2 are the elevations of sections 1 and 2 respectively.
hf is the head loss due to friction.
g is the acceleration due to gravity.
As the water level in the tank is constant, the pressure at section 1 and 2 will be atmospheric pressure. Therefore,
p1 = p2 = atmospheric pressure
Also, the head loss due to friction can be neglected as the orifices are small.
Thus, the Bernoulli's equation reduces to:
v1^2/2g + z1 = v2^2/2g + z2
As the discharge through both the orifices is the same, we have:
v1A1 = v2A2
Where,
A1 = cross-sectional area of the first orifice = πd1^2/4
A2 = cross-sectional area of the second orifice = πd2^2/4
Substituting the values of A1 and A2 in the above equation, we get:
v1d1^2 = v2d2^2
Substituting this in the Bernoulli's equation, we get:
d1^2/d2^2 = h2/h1
Substituting the given values, we get:
d1^2/d2^2 = 4
Taking the square root of both sides, we get:
d1/d2 = 2
Therefore, the ratio of the diameters d1 and d2 will be 2:1. Hence, option (C) is the correct answer.
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Community Answer
Two small circular ofifices of diameters d1 and d2 are placed on one s...
Since discharge remains constant.
Q1 = Q2,
A1 v1 = A2 V2,
Substitute the equation.
A1/A2 = (√h2/√h1).
Q1 = Q2,
A1 v1 = A2 V2,
Substitute the equation.
A1/A2 = (√h2/√h1).
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Two small circular ofifices of diameters d1 and d2 are placed on one side of a tank at depths of 25 cm and 1 m respectively below a constantsurface of water. If the discharges through theorifice are the same, then the ratio of the diameters d1 and d2 will bea)1 :2b)1: √2c)√2 :1d)2 : 1Correct answer is option 'C'. Can you explain this answer?
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Two small circular ofifices of diameters d1 and d2 are placed on one side of a tank at depths of 25 cm and 1 m respectively below a constantsurface of water. If the discharges through theorifice are the same, then the ratio of the diameters d1 and d2 will bea)1 :2b)1: √2c)√2 :1d)2 : 1Correct answer is option 'C'. 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 ofifices of diameters d1 and d2 are placed on one side of a tank at depths of 25 cm and 1 m respectively below a constantsurface of water. If the discharges through theorifice are the same, then the ratio of the diameters d1 and d2 will bea)1 :2b)1: √2c)√2 :1d)2 : 1Correct answer is option 'C'. 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 ofifices of diameters d1 and d2 are placed on one side of a tank at depths of 25 cm and 1 m respectively below a constantsurface of water. If the discharges through theorifice are the same, then the ratio of the diameters d1 and d2 will bea)1 :2b)1: √2c)√2 :1d)2 : 1Correct answer is option 'C'. Can you explain this answer?.
Two small circular ofifices of diameters d1 and d2 are placed on one side of a tank at depths of 25 cm and 1 m respectively below a constantsurface of water. If the discharges through theorifice are the same, then the ratio of the diameters d1 and d2 will bea)1 :2b)1: √2c)√2 :1d)2 : 1Correct answer is option 'C'. 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 ofifices of diameters d1 and d2 are placed on one side of a tank at depths of 25 cm and 1 m respectively below a constantsurface of water. If the discharges through theorifice are the same, then the ratio of the diameters d1 and d2 will bea)1 :2b)1: √2c)√2 :1d)2 : 1Correct answer is option 'C'. 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 ofifices of diameters d1 and d2 are placed on one side of a tank at depths of 25 cm and 1 m respectively below a constantsurface of water. If the discharges through theorifice are the same, then the ratio of the diameters d1 and d2 will bea)1 :2b)1: √2c)√2 :1d)2 : 1Correct answer is option 'C'. Can you explain this answer?.
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