Hi everyone,
I was calculating the critical valve closing time for a water hammer case using the Caesar manual formula, which is as under.

The speed of sound in the fluid can be estimated from
c = [Ef / (ρ + ρ(Ef / E) (d/t) )] 0.5
Where:
Ef - is the bulk modulus of the fluid (313000 psi)
E - is the modulus of elasticity of the pipe (30E6 psi)
d - is the pipe mean diameter
t - is the pipe wall thickness
ρ - is the fluid density (62.4 lbm/ft3)

Step 1:
ρ + ρ(Ef / E)(d/t) = 62.4 lbm/ft3 [1 + (313000/30E6) (8.625 -0.322)/0.322 ] = 79.1875 lbm/ft3

Step2:

c = (313000 lbf/ in2) (ft3/79.1875 lbm) (32.2 lbm ft/lbf sec2) (144in2 /ft2)1/2 = 4281 ft/sec

Now my query is.

In step 1 of calculation he is calculating as per the formula but in step 2 there is introduction acceleration due to gravity factor 32.2 lbm ft/lbf sec2 which does not figure anywhere in the formula for c given above.
Is the formula incorrect and if it correct why did he introduce this factor.

Formula is correct.

32.2 lbm ft/lbf sec2 is conversion factor between pound-mass (lbm)
and pound-force (lbf)

Regards,

Hi danb,
i think the formula should be dimensionally correct with out using the coversion factor.

No, it is more complicated than this.

Read this one and maybe you will understand.


http://instruct1.cit.cornell.edu/courses...f%20Conversions


It is just a different philosophy of countries that use Imperial Units. Maybe for us (that are using SI system) is strange, but it is the way it is.

Maybe someone that live in a country that use this System can explain better.

Regards,

Or to give you another example:
If you have F=p x A

and you have p=1 bar and A=1m2

In order to have the force in N you have to do

F= 0.1 N/mm2 x 1000000 mm2=100000 N

yet the formula remain F = p x A

Hope is clear now