You are trying to catch butterflies using a net whose rim is about 12.0 cm in ra

Question

You are trying to catch butterflies using a net whose rim is about 12.0 cm in radius. As you swing the net, there is a rush of air passing through it. You can describe the flow of air in terms of the momentum density (momentum per unit volume) of the air molecules, and in fact, you can depict the air molecules' flow as a set of "air field" lines. As the air passes through your net, the air field will be approximately uniform, flowing directly into the net's metal hoop (the field lines would be perpendicular to the net's metallic hoop). You know that the mass density of air in typical conditions is close to 1.3 kg/m^3. You guesstimate that the speed of the net through the air as you swung it was about 3.0 m/s. What is the flux of the air field (the momentum density) through your net? That is, how much of air mass is moving through your net per second?

Explanation / Answer

use the formula for Volume f flow rate as dV/dt = Av

where A is area and v is speed

from Density D = mass/VOlume

so Volume V = M/D

so

dM/dt = A v * D

dM/dt = 4pi r^2 * 3 * 1.3

dM/dt = (4*3.14 * 0.12 * 0.12 *3*1.3)

dM/dt = 0.705 kg/s or 705 gm/s

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