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Chapter 7: Problem 67

A dam spillway is \(40 \mathrm{ft}\) long and has fluid velocity of \(10 \mathrm{ft} / \mathrm{s}\) Considering Weber number effects as minor, calculate the corresponding model fluid velocity for a model length of \(5 \mathrm{ft}\).

Short Answer

Expert verified
The model's fluid velocity is \(80 \mathrm{ft}/\mathrm{s}\).

Step by step solution

01

Understand the Reynolds model law

The Reynolds model law is a dimensionless parameter that describes the flow regime in fluid dynamics. It's a ratio between inertial forces and viscous forces and is calculated as: \( Re = \frac{VDρ}{μ} \), where V is velocity, D is diameter (or any characteristic length), ρ is fluid density, and μ is dynamic viscosity. In model studies, it's assumed that the model and prototype have the same Reynolds number.
02

In this case, disregard density and viscosity

In many problems, it's reasonable to assume that the model and prototype are made of the same material and therefore have the same density and viscosity. Thus, we can simplify the Reynolds model law formula as follows: \( V_mD_m = V_D \).
03

Calculate the modeled fluid velocity

Reformulate the simplified Reynolds model law formula for the modeled fluid velocity. We get: \( V_m = \frac{V_D}{D_m} \). Now, substitute the given values: \( V_m = \frac{10 ft/s * 40 ft}{5 ft} = 80 ft/s \).

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Most popular questions from this chapter

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