How Can I Calculate the Downward Force on a Helicopter Using a Column of Air?

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SUMMARY

The discussion focuses on calculating the downward force exerted by a helicopter that maintains a stationary position by pushing air downward. Given a total mass of 1000 kg and an effective diameter of 6 m for the air column, the density of air is specified as 1.2 kg/m³. The solution involves determining the downward velocity of the air, which is calculated to be 17.2 m/s. The key formula to derive the force on the air column is based on the relationship between mass flow rate and velocity.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Knowledge of fluid dynamics, specifically Bernoulli's principle
  • Familiarity with the concept of mass flow rate
  • Basic algebra for solving equations
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  • Study the derivation of the mass flow rate formula in fluid dynamics
  • Learn about Bernoulli's equation and its applications in helicopter aerodynamics
  • Explore the relationship between pressure, force, and area in fluid systems
  • Investigate the effects of varying air density on helicopter lift
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Homework Statement


going through my a level text i found a prob i cannot solve


Homework Equations


1) a helicopter of total mass 1000kg is able to remain in a stationary position by imparting a uniform downward velocity to a cylinder of air below it of effective diametre 6m. Assuming the density of air to be 1.2 kg/m^3, calculate the downward velocity given to the air


The Attempt at a Solution


m=1.2*28.27= 33.92 kg
-m2a2=m1a1
stuck i know the ans is 17.2 m/s but i don't know how to get it
 
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what is the formula to calculate the force on a column of air of known density and cross sectional area??
once you figure out that formula ask yourself

what is the downward force on the helicopter?



if the helicopter is to stay in one place what forces must be equal in magnitude and opposite in direction?
 

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