Wind blows and pasts a banner causes it to flutter. The fluttering frequency f is a function of the wind speed V, the air density ρ, the acceleration of gravity g, the length of the banner L and the “area density” of the flag material ρA (with dimensions of ML-2 ). In order to estimate the flutter frequency of a large banner with L = 40 ft in a V = 30 ft/s wind, a small banner with L = 4 ft is to be tested in a wind tunnel. (a) What is the area density of the small banner when the large banner has area density of 0.006 slugs/ft2? (b) What should the wind tunnel velocity be to test the small model? (c) It has been shown that the small banner flutters at 6 s-1 when the same area density and wind tunnel velocity are used in parts (a) and (b). In this case, what is the fluttering frequency of the large banner?

Wind blows and pasts a banner causes it to flutter. The fluttering frequency f is a function of the wind speed V, the air density ρ, the acceleration of gravity g, the length of the banner L and the “area density” of the flag material ρA (with dimensions of ML-2 ). In order to estimate the flutter frequency of a large banner with L = 40 ft in a V = 30 ft/s wind, a small banner with L = 4 ft is to be tested in a wind tunnel. (a) What is the area density of the small banner when the large banner has area density of 0.006 slugs/ft2? (b) What should the wind tunnel velocity be to test the small model? (c) It has been shown that the small banner flutters at 6 s-1 when the same area density and wind tunnel velocity are used in parts (a) and (b). In this case, what is the fluttering frequency of the large banner?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.8P

See similar textbooks

Similar questions

5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.
A 1:20 scaled-down model of a hydrofoil is tested in a water channel, at a velocity of 0.179 m/s. At this velocity, a drag force of 2.2 N is measured. Determine the drag force of the original hydrofoil, at a velocity of 0.8 m/s.
A model of the Airbus 320 is tested in a wind tunnel using air at standard conditions. If the tunnel airspeed is 50m/s, calculate the water speed if the same model is to be tested in a water tunnel atdynamically similar conditions. Take mair=1.73 x 10-5Pa.s, mwater=10-3Pa.s, rair=1.225kg/m3 andrwater=1000 kg/m3.
a test tank will be used to measure the drag of a scale model ship 0.8 m long. This model bears full resemblance to a 40 m long prototype ship that was designed to sail at a speed of 10 m / s. a) model speed b) the ratio between model and prototype drag windows c) a ratio between the powers needed to overcome the drag of the model and the prototype take the number of froud into account in your analysis.
The New England Merchants Bank Building in Boston is 152 m high. On windy days it sways with a frequency of 0.17 Hz, and the acceleration of the top of the building can reach 2.0% of the free-fall acceleration, enough to causediscomfort for occupants. What is the total distance, side to side, that the top of the building moves during such an oscillation?
The drag equation for the Gofaster 172 is: D = 0.0003v2A. D is drag in pounds; v is airspeed in feet/second; and A is aircraft frontal area in square feet. At maximum airspeed, D = 140 lbs. How much does max airspeed INCREASE if the fuselage is narrowed such that frontal area A is reduced from 16 ft2 to 14 ft2? Give the answer in ft/sec AND mph. drag is 140 lbs. at maximum airspeed, regardless of frontal area. the question is: what is the INCREASE in max airspeed, not what is the max airspeed.
You are given a drone with an average chord length of 8 in., a wingspan of 2.5 ft, and a weight of 300 g. Based on figure 2, would it stay in the air at a speed of 5 m/s? (Assume ρ=1.225 kg/m3 and Nu=1.516*10-5 m^2/s)
An air hockey puck has a mass of 50 g and is 9 cm in diameter. When placed on the air table, a 40 degrees C air film, of thickness 0.12 mm-thickness forms under the puck. a) Using Sutherlands law, what is the viscosity of the air? b) If the puck is travelling at 10 m/s, assuming a linear velocity profile, what is the force on the puck due to shear stress? c)What is the terminal velocity of the puck?
While preparing an experiment of a scale model submarine in a wind tunnel, for conditions of dynamic similarity, it is calculated that the wind speed is required to be 120 m/s. Which one of the following options will not help to reduce the air velocity of the wind tunnel? A) Lowering the design velocity of the prototype (full scale) submarine B) Increasing the pressure of the air used in the wind tunnel c) Increasing the size of the scale model D) Decreasing the density of air used in the wind tunnel E) Reducing the temperature of the air used in the wind tunnel
A student needs to measure the drag on a prototype of characteristicdimension d p moving at velocity U p in air at standardatmospheric conditions. He constructs a model ofcharacteristic dimension d m , such that the ratio d p / d m issome factor f . He then measures the drag on the model atdynamically similar conditions (also with air at standardatmospheric conditions). The student claims that the dragforce on the prototype will be identical to that measured onthe model. Is this claim correct? Explain.
The pressure coefficient is defined by the ratio between the static pressure difference and the dynamic pressure (pictured): Where P is the static pressure [Pa], P∞ is the reference static pressure [Pa], ρ is the density [kg/m3], and V is the velocity [m/s]. Using the primary dimensions and their units, show that the pressure coefficient is dimensionless.
Resistance R to the motion of a completely submerged body is given by R = ρV2 L2 φ , where ρ and ν are density and kinematic viscosity of the fluid while L is the length of the body and V is the velocity of flow. If resistance of a one-sixth scale airship model when tested in water at 10 m/s is 230 N, what will be the resistance in air of the airship at the corresponding speed? Kinematic viscosity of air is 13 times that of water and density of water is 810 times of air.