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In a 1 in 16 model of a spillway, discharge is 3 m3/s, then the corresponding discharge in prototype is
- a)1028
- b)3072
- c)12564
- d)50432
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a 1 in 16 model of a spillway, discharge is 3 m3/s, then the corres...
In a spillway the predominant force is gravity, therefore the Froude law will be applicable for the model and prototype study.
Froude Model Law:
Scale ratio for velocity (Vr = Vm/Vp) = (Lr)0.5
Scale ratio for time, Tr = (Lr)0.5
Scale ratio for discharge, Qr = (Lr)2.5
Scale ratio for Force, Fr = (Lr)3
Scale ratio for Power, Pr = (Lr)3.5
Therefore,
Froude Model Law:
Scale ratio for velocity (Vr = Vm/Vp) = (Lr)0.5
Scale ratio for time, Tr = (Lr)0.5
Scale ratio for discharge, Qr = (Lr)2.5
Scale ratio for Force, Fr = (Lr)3
Scale ratio for Power, Pr = (Lr)3.5
Therefore,
Most Upvoted Answer
In a 1 in 16 model of a spillway, discharge is 3 m3/s, then the corres...
Calculation:
To find the corresponding discharge in the prototype, we need to understand the concept of scale ratio.
In a model, the scale ratio is defined as the ratio of a dimension in the model to the corresponding dimension in the prototype. In this case, the scale ratio is 1:16.
Let's assume the discharge in the prototype is Q (in m3/s).
The scale ratio can be used to relate the discharge in the model (Qm) to the discharge in the prototype (Qp) using the equation:
Qm/Qp = (Am/Ap) * (Vm/Vp)
Where:
Qm = discharge in the model
Qp = discharge in the prototype
Am = area in the model
Ap = area in the prototype
Vm = velocity in the model
Vp = velocity in the prototype
Since the scale ratio is 1:16, the area ratio (Am/Ap) and velocity ratio (Vm/Vp) will both be 1:16.
Solution:
Given that the discharge in the model is 3 m3/s, we can now solve for the discharge in the prototype.
Qm/Qp = (Am/Ap) * (Vm/Vp)
3/Qp = (1/16) * (1/16)
Cross-multiplying, we get:
Qp = 3 * (16 * 16)
Qp = 3 * 256
Qp = 768
Therefore, the corresponding discharge in the prototype is 768 m3/s.
Conclusion:
The correct answer is option B) 768 m3/s.
To find the corresponding discharge in the prototype, we need to understand the concept of scale ratio.
In a model, the scale ratio is defined as the ratio of a dimension in the model to the corresponding dimension in the prototype. In this case, the scale ratio is 1:16.
Let's assume the discharge in the prototype is Q (in m3/s).
The scale ratio can be used to relate the discharge in the model (Qm) to the discharge in the prototype (Qp) using the equation:
Qm/Qp = (Am/Ap) * (Vm/Vp)
Where:
Qm = discharge in the model
Qp = discharge in the prototype
Am = area in the model
Ap = area in the prototype
Vm = velocity in the model
Vp = velocity in the prototype
Since the scale ratio is 1:16, the area ratio (Am/Ap) and velocity ratio (Vm/Vp) will both be 1:16.
Solution:
Given that the discharge in the model is 3 m3/s, we can now solve for the discharge in the prototype.
Qm/Qp = (Am/Ap) * (Vm/Vp)
3/Qp = (1/16) * (1/16)
Cross-multiplying, we get:
Qp = 3 * (16 * 16)
Qp = 3 * 256
Qp = 768
Therefore, the corresponding discharge in the prototype is 768 m3/s.
Conclusion:
The correct answer is option B) 768 m3/s.
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In a 1 in 16 model of a spillway, discharge is 3 m3/s, then the corresponding discharge in prototype isa)1028b)3072c)12564d)50432Correct answer is option 'B'. Can you explain this answer?
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