Question
Download Solution PDFFor Froude model law, the scale ratio of force and scale ratio of length are related as: [Assuming the experiment is conducted on the same place and in the same fluid]
Answer (Detailed Solution Below)
Detailed Solution
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Froude Model Law
Definition: Froude Model Law is a similarity law used in fluid mechanics for the study and comparison of fluid flow phenomena in models and prototypes. It is primarily applied in cases involving gravitational forces, such as free surface flows, ship modeling, and open channel flows. The law states that the ratio of inertial forces to gravitational forces must be consistent between the model and the prototype to ensure dynamic similarity.
Working Principle: Froude Model Law is based on the principle that the Froude number (Fr), which is the ratio of inertial forces to gravitational forces, must remain the same for both the model and the prototype. The Froude number is given by:
Froude Number \(F_r = \frac{V}{\sqrt{gL}}\)
Where:
- v: Velocity of fluid
- g: Acceleration due to gravity
- L: Characteristic length
Dynamic similarity is achieved when the Froude number for the model and the prototype are equal:
\(\frac{V_m}{\sqrt {L_m g_m}} = \frac{V_p}{\sqrt{L_p g_p}}\)
From this, the relationships between various physical quantities such as velocity, time, force, and power can be derived.
Scale ratio of force = (Scale ratio of length)3
To understand why this is correct, let us analyze the relationship between force and length under Froude Model Law:
Force Relationship:
The force acting in a fluid flow is typically determined by the inertial forces and gravitational forces. According to Froude Model Law, the force scale ratio between the model and the prototype can be derived as follows:
- The inertial force is proportional to mass × acceleration.
- Mass is proportional to the volume, which scales with the cube of the length (l3).
- Acceleration, under Froude similarity, is proportional to g (gravitational acceleration), which does not change.
Therefore, the scale ratio of force (F) is proportional to the scale ratio of length (l) cubed:
Scale Ratio of Force = (Scale Ratio of Length)3
Last updated on Jul 15, 2025
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