21.
What is the lithostatic pressure at the base of a 35 km column of
granitic crust with an average density of 2.8 gm/cc ?
A)
8.2 kilobars B) 5.6 kilobars C) 9.8 kilobars D) 7.2 kilobars
Solution:
$Pressure (P) = \frac{Force}{ Area}$ --------------------------(1)
Force = mass * acceleration =mg---------------------(2)
Substitute eq(2) in eq(1)
$P=\frac{(m*g)}{ A}$ ------------------(3)
Mass(m) = density * volume =(ρ*V) --------------------(4)
Substitute eq(4) in eq(3)
$P=\frac{(ρ*V*g)}{A}$ ---------------------(5)
Volume= length * breadth* height
Area= length * breadth
substitute above values in eq(5)
Therefore, pressure(P)=(ρ*h*g)
Density (ρ)= 2.8 gm/cc =2800 kg/m^3
Height (h) = 35km = 35000m
Acceleration due to gravity (g) = 9.8 m/s^2
Pressure (P) = (2800*35000*9.8 ) kg/m.s^2
=960400000 kg/m.s2 (1 bar= 100000 Pa)
Litho-static pressure (P)= 9.6 Kilobar
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