ρ = B×(∆V/V) Bulk modulus of water, B = 2.2 × 109 Nm-2
ρ = 2.2 × 109× 10-3 = 2.2 × 106 Nm-2
Therefore, the pressure on water should be 2.2 ×106 Nm–2.
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Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.
Hydraulic pressure exerted on the glass slab, p = 10 atm = 10 × 1.013 × 105 Pa
Bulk modulus of glass, B = 37 × 109 Nm–2
Bulk modulus, B =
where,
∆V/V = Fractional change in volume
∴ ∆V/V = p / B
= = 2.73 × 10-5
Hence, the fractional change in the volume of the glass slab is 2.73 × 10–5.
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Anvils made of single crystals of diamond, with the shape as shown in Fig. 9.14, are used to investigate behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of 0.50 mm, and the wide ends are subjected to a compressional force of 50,000 N. What is the pressure at the tip of the anvil?
Diameter of the cones at the narrow ends, d = 0.50 mm = 0.5 × 10–3 m
Radius, r = d/2 = 0.25 × 10-3 m
Compressional force, F = 50000 N\
Pressure at the tip of the anvil is given by,
Therefore, the pressure at the tip of the anvil is 2.55 × 1011Pa.
ρ = B × (∆V/V)
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