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In a model test of spillway, the discharge and the velocity of flow over the model were 2 m3/s and 1.5 m/s respectively. The discharge over the prototype which is 36 times the model size will be ____ m3/s.
Correct answer is '15552'. Can you explain this answer?
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In a model test of spillway, the discharge and the velocity of flow ov...
Linear scale ratio 36
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In a model test of spillway, the discharge and the velocity of flow ov...
Given data:
Discharge in the model = 2 m³/s
Velocity of flow in the model = 1.5 m/s
Model size = 1
Prototype size = 36 (36 times the model size)
Calculation:
To find the discharge over the prototype, we can use the principle of similarity between the model and the prototype.
Principle of Similarity:
According to the principle of similarity, if two hydraulic models are geometrically similar, then the ratio of corresponding linear dimensions is equal to the ratio of corresponding quantities.
In this case, the model and the prototype are geometrically similar, with the prototype being 36 times larger than the model.
Ratios:
Ratio of linear dimensions = Prototype size / Model size = 36 / 1 = 36
Ratio of discharge = (Ratio of linear dimensions)^(exponent of discharge) = 36^x
We need to find the value of x, the exponent of discharge.
Using the principle of similarity for discharge:
In the model, the discharge is 2 m³/s.
In the prototype, the discharge is unknown (let's call it Q).
Using the principle of similarity, we have the following equation:
(Discharge in prototype) / (Discharge in model) = (Ratio of linear dimensions)^(exponent of discharge)
Q / 2 = 36^x
To solve for Q, we need to find the value of x.
Using the principle of similarity for velocity:
In the model, the velocity of flow is 1.5 m/s.
In the prototype, the velocity of flow is unknown (let's call it V).
Using the principle of similarity, we have the following equation:
(Velocity in prototype) / (Velocity in model) = (Ratio of linear dimensions)^(exponent of velocity)
V / 1.5 = 36^y
To solve for V, we need to find the value of y.
Relationship between discharge and velocity:
The relationship between discharge (Q) and velocity (V) is given by the equation:
Q = A * V
Where A is the cross-sectional area of flow.
Substituting the values:
From the equation Q / 2 = 36^x, we can rewrite it as Q = 2 * 36^x.
From the equation V / 1.5 = 36^y, we can rewrite it as V = 1.5 * 36^y.
Substituting these values into the equation Q = A * V, we have:
2 * 36^x = A * (1.5 * 36^y)
Simplifying the equation, we get:
2 * 36^x = 1.5 * A * 36^y
Dividing both sides by 36^y, we have:
2 * 36^(x-y) = 1.5 * A
Calculating the value of x-y:
From the given data, we know that the velocity of flow in the model is 1.5 m/s. Therefore, y = 0.
Substituting y = 0 into the equation 2 *
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In a model test of spillway, the discharge and the velocity of flow over the model were 2 m3/s and 1.5 m/s respectively. The discharge over the prototype which is 36 times the model size will be ____ m3/s.Correct answer is '15552'. Can you explain this answer?
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In a model test of spillway, the discharge and the velocity of flow over the model were 2 m3/s and 1.5 m/s respectively. The discharge over the prototype which is 36 times the model size will be ____ m3/s.Correct answer is '15552'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a model test of spillway, the discharge and the velocity of flow over the model were 2 m3/s and 1.5 m/s respectively. The discharge over the prototype which is 36 times the model size will be ____ m3/s.Correct answer is '15552'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a model test of spillway, the discharge and the velocity of flow over the model were 2 m3/s and 1.5 m/s respectively. The discharge over the prototype which is 36 times the model size will be ____ m3/s.Correct answer is '15552'. Can you explain this answer?.
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