Whats the calculations to size the expansion tank for specific system. Need details?

i have it image ( by scanner from collage ) .....4 papers too much to write .....if you know show me how to insert photos in answers and i will insert them 

There are three types of expansion tanks generally used.

1. for closed tanks with air / water interface 

Vt=Vs (( V2/ V1) -1))-3 @ DELTA t  / (Pa/P1)-(Pa/P2)

2. For Open tanks with air water interface 

Vt=Vs(V2/V1 -1)-3 @ delta t)

3. For Diaphragm tanks 

2.Vt=Vs (( V2/ V1) -1))-3 @ DELTA t    /  1-(Pa/P2)

@=Linear Coefficient of thermal expansion(in/in.ºF)=6.5E-  for steel      

Vt=Volume of expansion tank

Vs=Volume of water in system

t1=Lower temperature

 t2=Higher Temperature 

Pa=Atmospheric Pressure 

Pi=Initial Fill or minimum Pressure at tank

P1=Absolute Pressure at lower   temperature (Pi + Pa) i.e generally the head loss of pump calculated

Pmax=Maximum System Allowable Pressure

P2=Absolute Pressure at higher   temperature (Pmax + Pa)  generally1.5 to2 times P1

v1=Specific volume of water   at lower temperature  

v2=Specific volume of water   at higher temperature 

* If any one need the calculation sheet send me mail

Sizing is based on ASHRAE200 HVAC Systems & Equipment, Chap12, Hydronic Heating & Cooling System Design

Vt = Vs { (v2/v1) -3 * X * delta T } / {1 - (P1 / P2)}

where:

x=Linear Coefficient of thermal expansion(in/in.ºF)=6.5E-06  for steel      

Vt=Volume of expansion tank

Vs=Volume of water in system

t1=Lower temperature

 t2=Higher Temperature 

Pa=Atmospheric Pressure 

Pi=Initial Fill or minimum Pressure at tank

P1=Absolute Pressure at lower   temperature (Pi + Pa) 

Pmax=Maximum System Allowable Pressure

P2=Absolute Pressure at higher   temperature (Pmax + Pa) 

v1=Specific volume of water   at lower temperature  

v2=Specific volume of water   at higher temperature