Question

In low-speed external water flow over a bluff object, vortices are shed from the object. The vortex shedding produced by a particular object is to be studied in a water tunnel at a 1/4 scale model (model 1/4 the size of the prototype). After a dimensional study, it is found that the Pi terms of this phenomenon are the Reynolds number and the Strouhal number:Re = pVd/muSt = fd/Vwhere f is the frequency of the vortex shedding, V the velocity of the flow, d the characteristic length of the object, and p and mu the density and viscosity of the flow. 1. If the prototype speed is 7 m/s, determine the water velocity in the tunnel for the model tests. 2. If the model tests of part 1 produced a model shedding frequency of 200 Hz, determine the expected vortex shedding frequency on the prototype.

Answer 1

1) the water velocity in the tunnel for the model tests is 28 m/s

2) the expected vortex shedding frequency on the prototype is 12.5 Hz

Step-by-step explanation:

Given the data in the question;

1)

using the Reynolds number relation for prototype and model,

PpVpdp/mu(Prototype) = PmVmdm/mu(for model)

but we know that, density and viscosity in prototype and model will remain same so;

Vp × dp = Vm × dm

vm = Vp × dp/dm

we substitute

vm = 7 m/s × 4

vm = 28 m/s

Therefore, the water velocity in the tunnel for the model tests is 28 m/s

2)

we make use of the Strouhal number relation as given in the question;

fp × dp/Vp = fm × dm/Vm

frequency of the prototype will be;

fp = fm × dm/Vm / dp/Vp

we substitute

fp = 200 × 7 / ( 4 × 28 )

fp = 1400 / 112

fp = 12.5 Hz

Therefore, the expected vortex shedding frequency on the prototype is 12.5 Hz