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Chapter 7: Problem 59

A model hydrofoil is to be tested. Is it practical to satisfy both the Reynolds number and the Froude number for the hydrofoil when it is operating near the water surface? Support: your decision.

Short Answer

Expert verified
No, it is not practical to satisfy both the Reynolds number and the Froude number for a model hydrofoil operating near the water surface, as satisfying one can lead to the mismatch of the other.

Step by step solution

01

Understanding the Reynolds number

The Reynolds number (Re) is dimensionless. It is used in fluid mechanics to predict the transition from laminar to turbulent flow. Re = rho * L * U / mu, where rho is the fluid density, L is a characteristic linear dimension, U is the flow speed and mu is the dynamic viscosity.
02

Understanding the Froude number

The Froude number (Fr) is also dimensionless and is used in open channel flow description. Fr = U / sqrt(g * h), where U is the mean flow speed, g is the acceleration due to gravity, and h is a characteristic depth.
03

Assessing the compatibility of Reynolds and Froude numbers

It isn't practical to satisfy both the Reynolds and Froude numbers for a hydrofoil operating near the water surface. Here's why: The Reynolds number depends on speed, length (hydrofoil size), and fluid properties, while the Froude number depends on speed, gravity, and water depth. At a constant speed, we could match the Reynolds number in a model by adjusting the viscosity of the fluid. But then it would be impractical to match the Froude number because we don't usually control gravity and water depth when a hydrofoil runs. For the same reason, if we adjusted the depth to make the Froude numbers match, it's likely that the Reynolds numbers would then not match.

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Most popular questions from this chapter

A screw propeller has the following relevant dimensional parameters: axial thrust, \(F\), propeller diameter, \(D\), fluid kinematic viscosity, \(v,\) fluid density, \(\rho,\) gravitational acceleration, \(g,\) advance velocity, \(V,\) and rotational speed, \(N .\) Find appropriate dimensionless parameters to present the test data.

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