Deriving Expression for Average Drag on Object - Help Needed

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In summary, the conversation involves a person trying to derive an expression for the average drag on an object using the equation F_d = kv^2. They have decided to use an integral with t_f as the final time to find the average, but are having trouble evaluating it. They are then given a hint to use the equation F = m {dv/dt} = -kv^2 to solve for v(t).
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lithium123
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I'm trying to derive an expression for the average drag on an object, which is in the form $$F_d = kv^2.$$ To find the average, I decided to use $$\frac{1}{t_f} \cdot \int_{0}^{t_f} k v^2 \hspace{1mm} dt$$where t_f is the final time. I'm having trouble evaluating this. Can someone give me some insight?
 
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To find the time average, you need the integrand to be a function of time.
So you need an expression for v(t) .
 
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Additional hint, there's a cool equation called
$$F = m {dv \over dt} ... = -kv^2$$

Can you solve for v(t) given than equation?
 
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What is the formula for calculating average drag on an object?

The formula for calculating average drag on an object is FD = 0.5 * ρ * v^2 * CD * A, where FD is the drag force, ρ is the density of the fluid, v is the velocity of the object, CD is the drag coefficient, and A is the frontal area of the object.

What factors affect the average drag on an object?

The average drag on an object is affected by the density of the fluid, the velocity of the object, the drag coefficient, and the frontal area of the object. Other factors that can also impact drag include the shape of the object, surface roughness, and the fluid's viscosity.

How do you derive the expression for average drag on an object?

The expression for average drag on an object can be derived using the basic principles of fluid mechanics, such as Bernoulli's equation and the conservation of momentum. The derivation involves integrating the pressure and shear stress over the surface of the object and taking into account the different forces acting on the object.

What are the units for average drag?

The units for average drag are typically Newtons (N) or pounds (lbs) in the English system of units, and dynes (dyn) or grams (g) in the metric system of units.

Can the drag force on an object ever be zero?

In most cases, the drag force on an object cannot be zero, as there will always be some resistance from the fluid. However, in certain conditions, such as when an object is streamlined and moving at a constant velocity in a uniform fluid, the drag force can be reduced to a very small value.

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