Formulas for Ultrasonic Nondestructive Testing

Ultrasonic Key

V = velocity

Sin = sine of angle

Cos = cosine of angle

F = frequency

D = diameter of the transducer

BS = beam spread

λ = lambda or wavelentgh

p = density of the material

Z = acoustic impedance

dB = decible

NF = near field

Snell's Law:

Sin Θ1 / Sin Θ2 = V1 / V2 or Sin Θ2 = (Sin Θ1 * V2) / V1

Near Field:

NF = D2F / 4V or NF = D2 / 4λ

Beam's Spread:

BS = K * (V/DF) Note: K = 1.22 for 0 or null point K = 0.7 for 6 dB down

Wave Length:

λ = V/F

Acoustic Impedance:

Z = pV

Coefficient of Reflection:

((Z1 - Z2)2 / (Z1 + Z2)2)1/2

Decibel Ratio:

dB difference = 20 log10 (amplitude1 / amplitude2)

Flaw Location Depth:

Depth = cosθ of the angle X the sound path

Flaw Location from the exit point (surface distance):

Surface = Sound path X Sinθ of the angle

Formulas for Radiography Nondestructive Testing

Radiography Key

I = intensity

D = distance

Ug = geometric unsharpness

F = focal spot size

D = distance from the source to the source side of the object

T = the thickness of the object plus the distance from the object to the film

SDD = source to the detector (film) distance

Inverse Square Law:

I1 / I2 = D22 / D12 or I2 = I1 * D12 / D22


Ug = FT / D

Source to Detector Distance:

SDD = (FT / Ug) + T

To figure the strength of a source after a certain amount of time:

If an Ir. 192 source is 120 days old that is 1.6 half lives. So if the source was 100 curies at purchase the strength at 120 days is 39.6 curies.

100 * 0.51.6 = 39.6

If you have a 1/2" of lead and the half value layer is 0.2" you have 2.5 have value layers. If you had 60 Roentgens and put the 1/2" of lead at the point of 60 R you would now have 10.6 R on the opposite side of the lead.

60 * 0.52.5 = 10.6

Formulas for Magnetic Particle Nondestructive Testing

Magnetic Particle Key

N = number of turns in the coil

I = amperes

R = radius of the coil

L - is the usable length for the exam Ex. 9" each side of the center coil would allow for a max. length of 18" for ASME Section V; for ASTM E-1444 use ½ coil diameter each side of the coil

All formulas are for American units of measurement.

Testing with part next to the inside wall of the coil:

NI = 45000 / (L / D) or I = (45000 / (L / D)) / N

Testing with part centered in the coil and less than a 10% fill factor:

NI = (35000R) / ((6L / D) - 5)

Effective Diameter of hollow round parts:

(OD2 - ID2)1/2

Effective Diameter of hollow rectangular parts:

2(At - Ah / P)1/2

At = the area of the total cross section of the part and Ah = the area of the hollow cross section of the part