As shown below, a “noisemaker” B is towed behind a minesweeper A to set off enemy acoustic mines such as at C. The drag force of the noisemaker is to be studied in a water tunnel at 1/5 scale model (model 1/5 the size of the prototype). The drag force, FD, is assumed to be a function of the speed of the ship, V, the density, ρ, and viscosity, µ, of the fluid and the diameter, d, of the noisemaker. a) It has been shown that FD = f(V, ρ, µ, d). Express each parameter in terms of its primary dimensions using the MLT system b) How many dimensionless parameters are expected to fully describe this problem? Show your calculation. c) Using ρ, V, and d as repeating variables, and the linear equations method, develop the ∏1 term. Make ∏1 contain the dependent variable (FD). d) Using ρ, V, and D as repeating variables, and the linear equations method, develop the ∏2 term. Make ∏2 contain the non-repeating variable µ. e) The drag force of the noisemaker is to be studied in a water tunnel at a 1/5 scale model (model 1/5 the size of the prototype). If the prototype towing speed is 3 m/s, determine the water velocity in the tunnel for the model tests. You may assume the model fluid is the same as the fluid of theprototype. (f) If the model tests of part (e) produce a model drag of 900 N, determine the drag expected on the prototype. You may assume the model fluid is the same as the fluid of the prototype. (Solve all parts)
As shown below, a “noisemaker” B is towed behind a minesweeper A to set off enemy acoustic mines such as at C. The drag force of the noisemaker is to be studied in a water tunnel at 1/5 scale model (model 1/5 the size of the prototype). The drag force, FD, is assumed to be a function of the speed of the ship, V, the density, ρ, and viscosity, µ, of the fluid and the diameter, d, of the noisemaker.
a) It has been shown that FD = f(V, ρ, µ, d). Express each parameter in terms of its primary dimensions using the MLT system
b) How many dimensionless parameters are expected to fully describe this problem? Show your calculation.
c) Using ρ, V, and d as repeating variables, and the linear equations method, develop the ∏1 term. Make ∏1 contain the dependent variable (FD).
d) Using ρ, V, and D as repeating variables, and the linear equations method, develop the ∏2 term. Make ∏2 contain the non-repeating variable µ.
e) The drag force of the noisemaker is to be studied in a water tunnel at a 1/5 scale model (model 1/5 the size of the prototype). If the prototype towing speed is 3 m/s, determine the water velocity in the tunnel for the model tests. You may assume the model fluid is the same as the fluid of the
prototype.
(f) If the model tests of part (e) produce a model drag of 900 N, determine the drag expected on the prototype. You may assume the model fluid is the same as the fluid of the prototype.
(Solve all parts)
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