It is desired to study the velocity v of a fluid flowing in a smooth open channel. Assume that:

where r is the characteristic length of the channel cross-sectional area divided by the wetted perimeter, ρ is the fluid density, μ is the fluid viscosity, σ is the surface tension, and g is the acceleration of gravity.

a. Describe the appropriate pair of shape factors r₁ and r₂.

b. Show that:

c. Will it be practical to use the same fluid in the model and the prototype?

d. Suppose the surface tension σ is ignored and the design conditions are satisfied. If r_m= r, what is the equation for the velocity of the prototype? When is the equation compatible with the design conditions?

e. What is the equation for the velocity v if gravity is ignored? What if viscosity is ignored? What fluid would you use if you were to ignore viscosity?

Transcribed Image Text:

v = f(r. p. ,o,g)