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Question: How much pressure should be applied on a litre of water if it is to be compressed by 0.1%? (Bulk mo...

How much pressure should be applied on a litre of water if it is to be compressed by 0.1%?

(Bulk modulus of water, = 2100 MPa)

A

2100 kPa

B

210 kPa

C

2100 MPa

D

210 MPa

Answer

2100 kPa

Explanation

Solution

: Here, V=1litre=10−3m−3V = 1litre = 10^{- 3}m^{- 3}

B =2100 MPa = 2100 ×106Pa\times 10^{6}Pa

Volume strain

=ΔVV=0.1100=1×10−3= \frac{\Delta V}{V} = \frac{0.1}{100} = 1 \times 10^{- 3}

Bulk modulus, B = PΔV/V\frac{P}{\Delta V/V}

P=BΔVV=2100×106×1×10−3P = B\frac{\Delta V}{V} = 2100 \times 10^{6} \times 1 \times 10^{- 3}

=21×105Pa=2100×103Pa=2100KPa= 21 \times 10^{5}Pa = 2100 \times 10^{3}Pa = 2100KPa