Fluids Review Problems – Physics 2

 

1.      The density of mercury (like other substances) varies according to temperature.  At 0° C it is 13.595 g/mL and at 20° C it is 13.545 g/mL.  Considering how a mercury barometer functions, this would affect the reading of the height of the column of mercury.
(a) A temperature change of 0 to 20° C would cause how much apparent change in mm-Hg pressure (assuming the actual pressure is constant)? 
(b) One atmosphere of pressure is always quoted to be equal to precisely 760.0 mm-Hg – what density of mercury does this imply?

2.      The gravitational field strength on the surface of the Moon is 1.62 N/kg and the atmospheric pressure is zero (because there is no atmosphere).  Imagine a space outpost constructed there – a facility that contains breathable air at pressure 90.0 kPa. 
(a) What force would the air exert on a door with dimensions 1.1 m by 1.8 m?
(b) If a mercury barometer were inside the facility how many millimeters would it “read”?  
(c) Explain what would happen if the mercury barometer were taken outside on the Moon.

3.      To “tread water” one must create downward thrust with arms and legs to keep the entire head above water.  For a normal human body the head is 7.0% of a person’s mass and the body has an average density very near to that of water.  Base the following answers on a person with mass 70.0 kg.
(a) Determine the force of buoyancy on the person with only the head above water.
(b) What amount of downward thrust must be generated to keep the head above water?
(c) How far does the person sink into the water if not “treading”?
(d) The density of a person is so close to that of water that often the difference between floating or sinking (without moving arms or legs) depends simply on whether or not the person is holding a deep breath in the lungs – explain.

4.      Consider a spherical container of radius R made of a material with density ρ1.  The sphere has a sealed empty cavity of radius r inside it.  Derive an expression for the radius r that would prevent the sphere from sinking in water of density ρ2.  If the sphere has radius 10.0 cm and is made of iron, density 7800 kg/m3, how thin must the walls of this “shell” be?

5.      A kid doing a science experiment has a syringe with no needle attached.  He fills it with 30.0 mL of water and uses it like a squirt gun to fire water at a friend.  He fires the gun by pushing on the plunger, which has diameter 2.00 cm, and the water exits through an opening of diameter 1.5 mm.  The entire volume of water is fired in 1.5 s.
(a) Determine the flow rate of the water.
(b) Determine the speed of the water exiting the “gun”.
(c) Find the gauge pressure of the water inside the syringe.
(d) How much force must the kid exert on the plunger?  Disregard friction.
(e) How powerful is the kid wielding the squirt gun?

6.      Suppose a cylindrical stream of water of density ρ, speed v, and radius r is moving horizontally when it hits a wall.  Use Bernoulli’s equation to derive an expression for the force that the stream of water exerts on the wall.  Assume the water is essentially brought to rest by the wall (does not “splatter”).

 

 

 

 

Answers

1.      a. +2.8 mm-Hg
b. 13.01 g/mL

2.      a. 180 kN pushing outward
b. 4100 mm
c. In a normal circumstance the column of mercury in a barometer has atmospheric pressure at its base and zero pressure at its top surface.  However, if there is literally no atmospheric pressure acting on the mercury at the bottom of the column then the force of gravity would cause the mercury column to descend and empty the tube until all of the liquid would have the same level.

3.      a. 638 N, upward
b. 48.0 N
c. The person should sink entirely assuming density exactly equal to water.  However, there would not be a net force that would pull them to the bottom.  Instead the body would sink until fully submerged and then drag would cause it to stop moving just below the surface.
d. By holding air in the lungs the chest is expanded enough to significantly increase the overall volume of the body (or conversely it could be said that the inclusion of air decreases the average density of the body).  Taking a big breath of say 3.5 L has negligible effect on the overall mass of your body, but it increases the volume by essentially 3.5 L.  This would allow 3.5 L of body volume to float above water level – not quite enough to keep your head above water – hence the need to tread!

4.       

A hollow iron sphere of radius 10.0 cm and walls of thickness 0.44 cm would (barely) float.

5.      a. 2.0 × 10−5 m3/s
b. 11 m/s
c. 64 kPa
d. 20 N
e. 1.3 W

6.