Question

You are trying to duplicate the flight test conditions of an aircraft in a water tunnel. You know the Reynolds Number in the water tunnel needs to match the Reynolds number in the actual flight test. The aircraft was flying 200 m/sec at 7 km on a standard day. The mean chord of the aircraft is 2 m. (8.7) If the tunnel velocity is 27 m/sec, what is the proper length of the mean chord of the water tunnel model? (density of water is 1,000 kg/m³; viscosity of water is 1.12e⁻³ N sec/m²)

a. 0.6 meters
b. 0.9 meter
c. 2.5 meter
d. 3.1 meters

Answer 1

The proper length of the mean chord of the water tunnel model is approximately 0.6 meters. To find this, we use the Reynolds number equation and plug in the given values for density, velocity, and viscosity.

Step-by-step explanation:

To calculate the proper length of the mean chord of the water tunnel model, we need to match the Reynolds number in the water tunnel to the Reynolds number in the actual flight test. The Reynolds number is given by the formula:

Re = (Density of fluid) x (Velocity of fluid) x (Chord length of model) / (Viscosity of fluid)

Plugging in the given values, we have:

Re (flight) = (Density of air) x (Velocity of air) x (Chord length of aircraft) / (Viscosity of air)

Re (tunnel) = (Density of water) x (Velocity of water) x (Chord length of water tunnel model) / (Viscosity of water)

Since we know the Reynolds number in the flight test and the velocity and viscosity of the water in the tunnel, we can rearrange the equation to solve for the chord length of the water tunnel model:

Chord length of water tunnel model = (Re (flight) x Viscosity of water) / (Density of water x Velocity of water)

Plugging in the given values, we get:

Chord length of water tunnel model = (Re (flight) x 1.12e-3) / (1000 x 27)

Simplifying the expression, we find that the proper length of the mean chord of the water tunnel model is approximately 0.6 meters.