Brain Teasers

Temperature

Pascal’s Principle

Pneumatic Regeneration

Terminal Velocity

 

Ask Dan for the Answer

 

 

 

 

Temperature

 

1) What is the most likely temperature of slush in Boston, Massachusetts?

A)    None of the above.

B)    0

C)    32

D)   273.15

E)     491.67

F)     All of the above.

 

2) Explain your answer.

            Why slush?

 

 

            Why Boston, Massachusetts?

 

 

            Why or why not A)

 

 

            Why or why not B)

 

 

            Why or why not C)

 

 

            Why or why not D)

 

 

            Why or why not E)

 

 

            Why or why not F)

 

 

 

Pascal’s Principal

 

 

Blaise Pascal, the French physicist, found that a confined fluid transmits externally applied pressure uniformly in all directions and that the resultant force is applied perpendicular to the walls of the container and is described as the pressure per unit area of the container walls.

 

It is from this research that we have the simple formula of F=PA.

 

The two cylinders shown below have the same diameter and are connected to the same pressure source with no additional restrictions.

 

With this in mind, which of the two cylinders would exert the greater force?

 

Explain your answer.

 

 

 

 

Pneumatic Regeneration

 

 

In the following drawing, there is a cylinder with a piston having an area of 2 square inches and a rod with a cross sectional area of 1 square inch.   The area of the piston on the rod side that surrounds the rod is called the annulus and it is equal to the piston area minus the cross sectional area of the rod.  If the piston diameter is 2 square inches and the rod cross sectional area is 1 square inch, then the annulus area must be 1 square inch.

 

In the example, the pressure source is supplying air at 60 psig.  The supply is going to both ends of the cylinder.  We know that force is a factor of the pressure acting on an effected area.

 

At 60 psig:

 

How much force is acting on the piston?

 

How much force is acting on the annulus?

 

Would the cylinder:

               

Stay still?

               

Move to the right?

               

Move to the left?

 

How much force would be available? (ignore frictional losses)

 

 

 

 

 

 

It takes a certain amount of force to get a piston to begin to move.  This is because there are some forces acting against the piston even if there is no load on the rod.  There is the factor of inertia that requires a force to accelerate the mass of the piston and rod.  There is a frictional load from the piston and rod seals that tend to resist the start of motion.  This is sometimes referred to as “stiction”.  The accumulation of inertia and stiction is often described as the “breakaway” or the force required to start the piston moving without any external load.

 

In the following example, the same cylinder as in the above illustration is at rest.  It has a “breakaway” of 5 pounds.

 

At 14.7 psia:

 

How much force is acting on the piston?

 

How much force is acting on the annulus?

 

Would the cylinder:

               

Stay still?

               

Move to the right?

               

Move to the left?

 

 

 

In the last example, the same cylinder has a vacuum of -12 psig applied to both ports.

 

At -12 psig:

 

How much force is acting on the piston?

 

How much force is acting on the annulus?

 

Would the cylinder:

               

Stay still?

               

Move to the right?

               

Move to the left?

 

 

Terminal Velocity

 

When we speak of Terminal Velocity, we are not talking about the speed of the taxicabs at the airport.

 

We are talking about what happens when someone is skydiving.

 

A person weighing 150 pounds jumps out of an airplane at an elevation of 10,000 feet.  Using the formulas d = ˝ at2 and V = at, where:

d = distance in feet

a = acceleration of 32.2 ft/sec/sec

t = time in seconds

V = the change in velocity in feet per second

we find our jumper should be traveling at about 489 miles per hour when she reaches 2000 feet and pulls the rip-cord.

 

However, experience has shown that if she remains in a horizontal position, she will only attain a speed of about 120 miles per hour.  If she positions herself vertically, she may attain about 280 miles per hour.

 

1)      Why is it that her Terminal Velocity is so much less than the speed shown by the formulas?

 

 

 

2)      Why does she go faster when she is vertical than when she is horizontal?

 

 

 

Do not just say, “wind resistance”.  What is really going on here?