Question

Many cultures around the world still use a simple weapon called a blowgun, a tube with a dart that fits tightly inside. A sharp breath into the end of the tube launches the dart. When exhaling forcefully, a healthy person can supply air at a gauge pressure of 6.0 kPa.
What force does this pressure exert on a dart in a 1.4-cm-diameter tube?

Answer 1

Multiply the gauge pressure in Pascals (6000) by the tube's circular inner area cross section in square meters (pi D^2/4) to get the force in Newtons.

pi D^2/4 = 1.54*10-4 m^2

I get about 1 Newton, which is about 1/4 pound force.

Answer 2

Use the equation Pressure = Force / Area. Solve the equation for Force to get Force = Pressure * Area. Now, just plug in the values. Force = 0.006 Pa * (pi)0.008^2. Notice you need to divide the radius (0.008 m), not the diameter, in the equation for the area of a circle. The answer is 1.21 N.

Answer 3

Here's the actual answer.
Pressure = Force / Area
Force = Pressure * Area
Area = πr^2
1.4cm = 0.014m
0.014m/2 = 0.007m (this is the radius)
(π)(0.007^2) = 1.54 *10^-4 m^3 (this is the area)
6.0kPa = 6000Pa (this is the force)
(1.54*10^-4 m^3)(6000Pa) = 0.92N (this is the pressure, aka your answer)