In a 1:36 scale model test of a spillway, discharge of flow over the model is 6 m3/s. If the velocity of flow over model was found to be 5 knots, then the velocity of flow over prototype in m/s will bea)30b)15.45c)9d)24.36Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Scale Model Test

In a scale model test, a smaller version of the prototype is built and tested to gather information about the performance and behavior of the full-scale structure. The relationship between the model and the prototype is defined by the scale factor. In this case, the scale factor is 1:36.

Given Information

In the scale model test of a spillway:

Discharge of flow over the model = 6 m³/s

Velocity of flow over the model = 5 knots

Finding the Velocity of Flow over Prototype

We need to find the velocity of flow over the prototype, which is the full-scale structure. To do this, we can use the concept of similitude, which states that the ratios of corresponding quantities in the model and prototype should be equal.

Let's consider the velocity of flow over the prototype as Vp and the velocity of flow over the model as Vm.

Using the Discharge Equation

The discharge Q through a cross-section is given by the equation:

Q = A * V

Where:

Q is the discharge

A is the cross-sectional area

V is the velocity

Since the scale factor is 1:36, the cross-sectional area of the model is 1/36 times the cross-sectional area of the prototype:

Am = 1/36 * Ap

Substituting the values:

6 m³/s = (1/36 * Ap) * 5 knots

Converting Knots to m/s

To compare the velocities, we need to convert knots to m/s. 1 knot is equal to 0.5144 m/s.

Substituting the value of velocity in m/s:

6 m³/s = (1/36 * Ap) * 5 * 0.5144 m/s

Simplifying the Equation

Cancelling out the common factors:

6 = (1/36 * Ap) * 2.572

Multiplying both sides by 36:

6 * 36 = Ap * 2.572

Ap = (6 * 36) / 2.572

Ap ≈ 84.36 m²

Calculating the Velocity of Flow over Prototype

Now, let's substitute the value of Ap into the discharge equation for the prototype:

Qp = Ap * Vp

Since the discharge through the model and prototype is the same:

Qp = Qm

Ap * Vp =

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