A student team is to design a humanpowered submarine for a d

A student team is to design a human-powered submarine for a design competition The overall length of the prototype submarine is 2 24 m, and its student designers hope that it can travel fully submerged through water at 0.560 m/s The water is freshwater (a lake) at T = 15 degree C The design team builds a one-eighth scale model to test in their university\'s wind tunnel A shield surrounds the drag balance strut so that the aerodynamic drag of the strut itself does not influence the measured drag The air in the wind tunnel is at 25 degree C and at one standard atmosphere pressure At what air speed do they need to run the wind tunnel in order to achieve similarity0 5. The students from the previous problem measure the aerodynamic drag on their model submarine in the wind tunnel They are careful to run the wind tunnel at conditions that ensure similarity with the prototype submarine Their measured drag force is 2 3 N. Estimate the drag force on the prototype submarine at the conditions given in Problem #2

Solution

4.

For air at 1 atm and 25 C, we get density = P/RT = 101325 / (287*298) = 1.18 kg/m^3

To achieve dynamic similarity Reynolds number between model and prototype must be the same.

Re = rho*V*L/u

For water at 15C, rho = 1000 kg/m^3, u = 0.00115 Pa-s

For air, rho = 1.18 kg/m^3, u = 1.846*10^-5 Pa-s

So, 1000*0.56*2.24 / 0.00115 = 1.18*V*(2.24/8) / (1.846*10^-5)

V = 60.94 m/s