478 stimson: mercury vapor pump 



This problem is different from Langmuir's in requiring in the 

 mercury vapor pump the maintenance of a much larger pressure 

 difference by means of a continuous supply of momentum in a 

 manner analogous to the maintenance of a kite in air by the 

 employment of the momentum of the wind. To sustain this 

 large pressure difference a second stage is desirable, for could 

 such a pressure difference be sustained and high vacuum at- 

 tained with one stage, either a very large current of vapor would 

 be required or the pump would have to be made so small that 

 its speed would be very low. A second stage, on the contrary, 

 in order to pump all the gas discharged from a pump working 

 on high vacuum, need have only a hundredth the speed of the 

 high vacuum stage or even less. 



From dimensional reasoning it follows that whatever supports 

 the pressure must have the same physical dimensions. Pres- 

 sure has the dimensions of force per unit area and force has the 

 dimensions of mass times velocity divided by time : 



p =f/p = mv/tl 2 . 



In order to make p large, I 2 , the cross sectional area across which 

 the stream of mercury vapor acts, can be made small. It is well 

 known that a gas will flow through an orifice with a limiting- 

 velocity, which is the velocity of sound, if the ratio of final to 

 initial pressure of the gas on the two sides of the orifice is less 

 than a certain limiting fraction. This fraction for mercury vapor 

 is about 0.49 and the velocity of sound referred to is that veloc- 

 ity determined by the temperature of the vapor in the orifice 

 where it is adiabatically expanded to this limiting pressure. It 

 appears then that mercury vapor can be expelled through an 

 orifice with the velocity of sound by a boiler pressure a little 

 more than twice the pressure of the supporting vacuum. When 

 the boiler pressure is sufficient the velocity may be increased 

 beyond the velocity of sound, as is done in the steam turbine, 

 by an expanding nozzle, but such an enlargement requires an 

 increased working cross section over which the pressure must be 

 supported, thus limiting the advantage of the increased velocity. 

 The term m/t can be increased by increasing the boiler pressure, 



