Bulk Modulus Calculator:
Enter the values of initial volume, V1(m3), final volume, V2(m3), pressure, P2(Pa) and P1(Pa) to determine the value of Bulk Modulus, B(Pa).
Bulk Modulus Formula:
The Bulk Modulus (B) is a fundamental property of materials that quantifies their resistance to uniform compression under applied pressure. It is a measure of a material’s ability to maintain its volume when subjected to external pressure. Bulk modulus is particularly relevant in fluid mechanics, material science, and engineering applications, helping describe how materials deform under compressive forces.
The bulk modulus is defined as the ratio of the change in pressure to the relative volumetric deformation it causes. A higher bulk modulus indicates that the material is less compressible and more resistant to changes in volume under pressure. The unit of bulk modulus is typically Pascals (Pa) or N/m2.
When a material is subjected to an initial pressure P1(Pa) and its initial volume is V1(m3), any increase in pressure to P2(Pa) leads to a decrease in the material’s volume to V2(m3). The bulk modulus is calculated using these changes.
Bulk Modulus, B(Pa) in Pascals equals the negative product of the initial volume, V1(m3) in cubic metres and the ratio of the change in pressure, (P2(Pa) − P1(Pa)) in Pascals to the change in volume, (V2(m3) − V1(m3)) in cubic metres.
Bulk Modulus, B(Pa) = – V1(m3) * ((P2(Pa) − P1(Pa)) / (V2(m3) − V1(m3)))
B(Pa) = bulk modulus in Pascals, Pa.
V2(m3) − V1(m3) = initial and final volume in cubic metres, m3.
P2(Pa) − P1(Pa) = initial and final pressure in Pascals, Pa.
Bulk Modulus Calculation:
1.A material with an initial volume 0.02m3 is subjected to an increase in pressure from 100,000Pa to 300,000Pa. The final volume decreases to 0.019m3. Find the bulk modulus.
Given: V1(m3) = 0.02m3,V2(m3) = 0.019m3, P1(Pa) = 100000Pa, P2(Pa) = 300,000Pa.
Bulk Modulus, B(Pa) = – V1(m3) * ((P2(Pa) − P1(Pa)) / (V2(m3) − V1(m3)))
B(Pa) = – 0.02 * ((300000 – 100000) / (0.019 – 0.02))
B(Pa) = – 0.02 (200000 / (- 0.001))
B(Pa) = 0.02 * 200000000
B(Pa) = 4000000Pa.
2.A material with an initial volume 0.05m3 has a bulk modulus 2,000,000Pa. It is subjected to a pressure change from 50,000Pa to 250,000Pa. Find the final volume.
Given: V1(m3) = 0.05m3,B(Pa) = 2000000Pa, P1(Pa) = 50000Pa, P2(Pa) = 250,000Pa.
Bulk Modulus, B(Pa) = – V1(m3) * ((P2(Pa) − P1(Pa)) / (V2(m3) − V1(m3)))
V2(m3) = V1(m3) + (- V1(m3) * (P2(Pa) − P1(Pa)) / B(Pa))
V2(m3) = 0.05 + (- 0.05 * (25000 – 50000) / 2000000)
V2(m3) = 0.05 + (- 0.05 * (200000) / 2000000)
V2(m3) = 0.05 + (- 10000 / 2000000)
V2(m3) = 0.05 – 0.005
V2(m3) = 0.045m3.