Pressure in Fluids

      
Introduction

                              Force        F                                      N               lbs
Pressure  = P  =   ---------  =  ---                      Units     -----    or   -----------       1 N/m²  =  1 Pascal  =  1 Pa
                               Area         A                                     m²             in²     

   
1.00 atmosphere  =  average air pressure at sea level

1.00 atm  =  101.3 kPa  =  1013 millibar  =  760.00000 torr =  760.00000 mm Hg  =  14.7 PSI

Fluids exert the same pressure in all directions.  If an object underwater did not get the same pressure from all directions, it would be forced in the direction indicated by the net force.  

The force exerted is always perpendicular to the point of contact on a surface.

Using the diagram to the left to calculate the pressure at a depth of h.

The pressure is due to the weight of the column of water over the area A.

   
         F        Ahg
P  =  ---  =  ----------  =  gh
         A            A  
    

/\P  =  g/\h         is the average density.  Density changes slightly with 
                            depth.

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Problems

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Answers

1.	Calculate the pressure exerted by Lisa, 50.0 kg, standing in spike-heels with only the heel in contact with the floor.  Each heel is a square 0.250 cm on a side.  Compare this pressure to a 1750 kg elephant with each foot  25.0 cm x 30.0 cm.
	F           50.0 kg x 9.80 m s -2  P  =  -----  =  ----------------------------------  =    3.92 x 10 7 Pa         Lisa           A          2 x 0.0025 m x 0.0025 m                F           1750 kg x 9.80 m s -2  P  =  -----  =  ----------------------------------  =    5.72 x 10 4 Pa        Elephant           A          4 x 0.250 m x 0.300 m     P Lisa              3.92 x 10 7 Pa -------------  =  ---------------------  =  685      Lisa's pressure is 685 times greater than the Elephant's pressure. P Elephant          5.72 x 10 4 Pa
2.	(a)  Calculate the total force due to atmospheric pressure at sea level on a table top that is 1.25 m x 1.80 m. (b)  Calculate the total force on the underside of the table top.
	F P  =  ----   =>  F  =  PA  =  1.013 x 10 5  N  m -2  x  1.25 m  x  1.80 m  =  2.28 x 10 5 N          A     An equal pressure of 2.28 x 10 5 N is applied to the underside of the table.
3.	In one of the Tarzan movies, he hid from captures by hiding underwater and breathing through a thin reed.  The greatest pressure difference before lungs collapse is 0.50 atmospheres.  What is his maximum depth?
	101300 Pa 0.50 atm x ---------------   =  50700 Pa  =  P                       1 atm     P  =  gh                              Solve for h.                P                       50700 N  m -2   h  =  ------  =  ---------------------------------------------  =  5.17 m          g         1.00 x 10 3 kg m -3  x  9.80 m s -2
4.	The greatest depth a diver has achieved holding his breath and returning to the surface is 184 m.  What was the pressure on the diver at his maximum depth?  He was in saltwater not freshwater. Physics Charts - Densities of Substances
	P  =  gh   =  1.025 x 10 3 kg m -3  x  9.80 m s -2  x  184 m  =  1850 kPa

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