Questions regarding equation for circular mode frequency

[GenSoft3d]

I'm trying to determine the circular mode frequency for an open-ended pipe using the following equation and could use some clarification:

f = (t/(2*d^2))*SQRT(E/density)

f - frequency
E - modulus of elasticity
d - mean diameter
t - wall thickness

My first question is; do I need to multiply the values inside the SQRT by gravity (386.4 in/sec2) in order to get the correct units for this equation?

Also, is the frequency noted here (f) referring to radian per second and will I need to divide it by 2*pi in order to convert it to cycles per second?

Any help would be greatly appreciated. Thanks!

 

[nasu]

It has the right units as it is. The part with the square root is the speed of sound in the material of the pipe.

 

[AlephZero]

My first question is; do I need to multiply the values inside the SQRT by gravity (386.4 in/sec2) in order to get the correct units for this equation?

You need to use consistent units. SI units (kg/m^3 and Pascals) are consistent. Units that mix up "pounds mass" and "pounds force" are not.

Also, is the frequency noted here (f) referring to radian per second and will I need to divide it by 2*pi in order to convert it to cycles per second?

Yes.

 

[GenSoft3d]

Thanks so much for the help on this... I really appreciate it!

I may be asking the same question twice but can you verify for me if I need to apply the same freq conversion for Hz (/2*pi) to the following equation used to determine transverse waves in a pipe with free ends?

fn=pi*vKm^2/8L^2

where:

v= √ (Y/r)
Y= Young's modulus
r= density
K= 1/2 * √ (a^2 + b^2)
a= inside radii
b= outside radii
L= length
m= 3.0112, 5, 7...(2n+1)

 

[nasu]

Thanks so much for the help on this... I really appreciate it!

I may be asking the same question twice but can you verify for me if I need to apply the same freq conversion for Hz (/2*pi) to the following equation used to determine transverse waves in a pipe with free ends?

fn=pi*vKm^2/8L^2

where:

v= √ (Y/r)
Y= Young's modulus
r= density
K= 1/2 * √ (a^2 + b^2)
a= inside radii
b= outside radii
L= length
m= 3.0112, 5, 7...(2n+1)

This gives the frequency in hertz, according to Ross - Percussion instruments.