A 1: 15 dynamically similar scale model of a boat is towed through water at a sp

Question

A 1: 15 dynamically similar scale model of a boat is towed through water at a speed of 1.2 m/s. The model has a drag of 0.44 N due to the surface waves that radiate away from the hull. What is the drag on the real boat? Note that a problem of this nature can be done in 2 ways. Method 1: Construct a list of all independent variables that you think might be important, determine your Pcy-groups, and then neglect all the ones with minor forces. For simplicity, use a Transperth ferry as your prototype. Method 2: Use your understanding of our four main dimension- less parameters (Re, Fr, Bo, We) to determine which one is the relevant matching parameter. You should work through this problem using both of these methods, and show that they give exactly the same result (shown below) (Answer: 1485 N)

Explanation / Answer

The dynamic similarity is said to exist between the model and prototype if the ratios of the corresponding forces(and also directions) acting at the corresponding points are equal.

In this problem, if we observe inertia force opposite to the direction of the acceleration of the ship and gravity forces are acting. In this situation, Froude model law is to be used.

Given,

scale ratio of length, Lr=15

speed of model, Vm =1.2m/s

drag or force required to tow the model, Fm=0.44N

Let force or drag required for ship= Fp

Force scale ratio in Froude model law is given by equation

Fr= Fp/Fm= Lr

Fp= Fm * Lr3 = 0.44 * 153 = 1485N

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