Hurricane Physics: Part 3

As was mentioned in Part 2, it is now time to talk about pseudo forces.  The two most well known pseudo forces are centrifugal force and Coriolis force.  Remember, pseudo means “not real”.  So, let us start with centrifugal force.

Centrifugal Force


A good example to start with is the impeller of a centrifugal pump.  Please refer to the above idealized diagram.  In position 1, a package of fluid will enter the impeller area through an eye hole at the center of the impeller disk.  The impeller disk is spinning as shown by the red line.  The fluid is immediately batted forward, more or less, 90 degrees to the impeller.

However, the impeller disk is spinning at a very fast rate, so the impeller catches up to the fluid package and hits it again, at position 2.  The package goes flying off at 90 degrees.  Finally at position 3, the impeller hits the package at the tip of the impeller.  The package does leave the disk 90 degrees to the impeller, but essentially in a tangential fashion to the spinning disk.

What is important to note here is that the actual process is not happening in stages as shown above; rather, it is happening in a completely continuous fashion through the length of the impeller.  For that reason, the particle appears to be moving radially, when in fact it is moving tangentially.  An illusion is created where a force seems to pushing the particle outward in a radial fashion.  We call that centrifugal force.  Centri refers to center and fugal refers to escaping – center escaping.


So why is that important?  Let us say you wish to put a satellite in orbit, as shown in the figure above.  The gravity of the earth is applying centripetal force to keep the satellite in orbit (centri referring to center and petal referring to moving – center moving).  Centripetal force is real, not a pseudo force.  The catch is that from Newtonian physics, we know that a system at equilibrium must have a force balance sum equal to zero.  Say hello to centrifugal force:  centripetal force must equal centrifugal force.

You can see from the diagram that the velocity of the satellite is moving tangentially to the circular path around the earth, that is one factor.  The other factor is the force being applied to the satellite by the earth.  There is no force pushing the satellite outwardly, it is actually falling; but the satellite’s tangential velocity perfectly balances with the gravity of the earth so that satellite travels in an orbit.  The pseudo force, centrifugal force, can be used to explain why the centripetal force does not pull the satellite to the ground

Centripetal force equals centrifugal force, or in other words, F = mg = mv^2/r.  The left side of the equation, mg, is the centripetal force and this equation can be used to determine at what velocity the satellite must be traveling such that orbit can be maintained.

Coriolis Force


The Coriolis force is also a pseudo force and similar to centrifugal force, just a little different.  Please observe the figure above.  Let us say that the school boy is on a merry-go-round, spinning as shown.  When the boy reaches the right side of the revolution, he is throwing a ball to the right in a radial direction.  The boy then rotates to the top of the ride while simultaneously the ball reaches its final destination.

As you can see from the diagram, the ball travels in a straight line.  The path of the ball is not affected by the fact that the boy is spinning.  The ball’s path is independent the moment it leaves the boys hand.  This is what is seen by the independent on-looker.  However, the boy does not see this.  He sees some mysterious force acting on the ball.

In the lower right hand corner is a depiction of what the boy sees as he rotates to the top of the merry-go-round.  To the independent observer, standing in the park, the ball is simply traveling in a straight line; but to the boy, the 90 degree rotation makes the ball appear to have an invisible force acting on it that makes the ball turn to the right.  That mysterious pseudo force is called the Coriolis force.  The expression for the Coriolis force is Fc = 2mwv, where m = mass of ball, w = angular velocity of the merry-go-round, and v = velocity of the ball.

The Coriolis force is what is at play during the formation of an hurricane.  I think the important thing to remember is that pseudo forces are not real.  Next time we shall discuss how natural phenomena come together to form the complexity of what is called a hurricane.


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