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A 1 m wide rectangular channel carries a discharge of 2m3s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to _______
Correct answer is '1.0694'. Can you explain this answer?
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A 1 m wide rectangular channel carries a discharge of 2m3s. The specif...
Given sub critical depth = 2 × super critical depth
y= super critical depth
Sub critical depth = 2 y
Super critical depth (y) = 0.5347
Sub critical depth = 2y = 2 × 0.5347 = 1.0694 m
y= super critical depth
Sub critical depth = 2 y
Super critical depth (y) = 0.5347
Sub critical depth = 2y = 2 × 0.5347 = 1.0694 m
Most Upvoted Answer
A 1 m wide rectangular channel carries a discharge of 2m3s. The specif...
Given data:
Width of rectangular channel (B) = 1 m
Discharge (Q) = 2 m3/s
To find: Subcritical depth (yc)
Concepts used:
Specific energy (E) = (y + V2/2g)
Critical depth (yc) = (Q2/gB3)1/3
Froude number (Fr) = V/√(gy)
Subcritical flow: Fr < />
Supercritical flow: Fr > 1
Calculation:
1. Calculation of critical depth (yc):
yc = (Q2/gB3)1/3
yc = (2*2/9.81*1)1/3
yc = 0.437 m
2. Calculation of specific energy (E):
Using the specific energy-depth diagram, let the specific energy be E1 and the corresponding depth be y1.
E1 = (y1 + V1^2/2g)
Given that the subcritical depth is twice the supercritical depth at E1. Let the supercritical depth be ysc and the corresponding velocity be Vsc.
ysc = y1/2
Fr = Vsc/√(gysc)
Fr = V1/√(gy1)
3. Calculation of velocity (V1) from discharge (Q):
Q = AV1
A = By1
Q = B*y1*V1
V1 = Q/(By1)
V1 = 2/(1*y1)
V1 = 2/y1
4. Calculation of velocity (Vsc) from Froude number (Fr):
Fr = Vsc/√(gysc)
Vsc = Fr*√(gysc)
Vsc = V1/2
5. Calculation of specific energy (E1):
E1 = (y1 + V1^2/2g)
E1 = (y1 + (2/y1)^2/2*9.81)
E1 = (y1 + 4/y1/19.62)
6. Calculation of specific energy (E2):
ysc = y1/2
Vsc = V1/2
E2 = (ysc + Vsc^2/2g)
E2 = (y1/2 + (2/y1/2)^2/2*9.81)
E2 = (y1/2 + 1/y1/19.62)
7. Equating E1 and E2:
(y1 + 4/y1/19.62) = (y1/2 + 1/y1/19.62)
Multiplying by 19.62*y1*2:
39.24 + 8 = 9.81*y1^2 + 39.24
9.81*y1^2 = 47.24
y1 = √(47.24/9.81)
y1 = 1.0694 m (approx)
Therefore, the subcritical depth (yc) is equal to 1.0694 m (approx).
Width of rectangular channel (B) = 1 m
Discharge (Q) = 2 m3/s
To find: Subcritical depth (yc)
Concepts used:
Specific energy (E) = (y + V2/2g)
Critical depth (yc) = (Q2/gB3)1/3
Froude number (Fr) = V/√(gy)
Subcritical flow: Fr < />
Supercritical flow: Fr > 1
Calculation:
1. Calculation of critical depth (yc):
yc = (Q2/gB3)1/3
yc = (2*2/9.81*1)1/3
yc = 0.437 m
2. Calculation of specific energy (E):
Using the specific energy-depth diagram, let the specific energy be E1 and the corresponding depth be y1.
E1 = (y1 + V1^2/2g)
Given that the subcritical depth is twice the supercritical depth at E1. Let the supercritical depth be ysc and the corresponding velocity be Vsc.
ysc = y1/2
Fr = Vsc/√(gysc)
Fr = V1/√(gy1)
3. Calculation of velocity (V1) from discharge (Q):
Q = AV1
A = By1
Q = B*y1*V1
V1 = Q/(By1)
V1 = 2/(1*y1)
V1 = 2/y1
4. Calculation of velocity (Vsc) from Froude number (Fr):
Fr = Vsc/√(gysc)
Vsc = Fr*√(gysc)
Vsc = V1/2
5. Calculation of specific energy (E1):
E1 = (y1 + V1^2/2g)
E1 = (y1 + (2/y1)^2/2*9.81)
E1 = (y1 + 4/y1/19.62)
6. Calculation of specific energy (E2):
ysc = y1/2
Vsc = V1/2
E2 = (ysc + Vsc^2/2g)
E2 = (y1/2 + (2/y1/2)^2/2*9.81)
E2 = (y1/2 + 1/y1/19.62)
7. Equating E1 and E2:
(y1 + 4/y1/19.62) = (y1/2 + 1/y1/19.62)
Multiplying by 19.62*y1*2:
39.24 + 8 = 9.81*y1^2 + 39.24
9.81*y1^2 = 47.24
y1 = √(47.24/9.81)
y1 = 1.0694 m (approx)
Therefore, the subcritical depth (yc) is equal to 1.0694 m (approx).
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A 1 m wide rectangular channel carries a discharge of 2m3s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to _______Correct answer is '1.0694'. Can you explain this answer?
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A 1 m wide rectangular channel carries a discharge of 2m3s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to _______Correct answer is '1.0694'. 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 A 1 m wide rectangular channel carries a discharge of 2m3s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to _______Correct answer is '1.0694'. 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 A 1 m wide rectangular channel carries a discharge of 2m3s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to _______Correct answer is '1.0694'. Can you explain this answer?.
A 1 m wide rectangular channel carries a discharge of 2m3s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to _______Correct answer is '1.0694'. 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 A 1 m wide rectangular channel carries a discharge of 2m3s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to _______Correct answer is '1.0694'. 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 A 1 m wide rectangular channel carries a discharge of 2m3s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to _______Correct answer is '1.0694'. Can you explain this answer?.
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