Assume the bulk modulus to be constant (= 310,000 lb/in^2) and find an expressio

Question

Assume the bulk modulus to be constant (= 310,000 lb/in^2) and find an expression for the pressure p as a function of depth h in the ocean. Use this expression and estimate the pressure assuming that density at zero depth (the surface) is: rho_0 = 2.0slug/ft^3. Now, assume a constant density of 2.0 slug/ft^3 and calculate the pressure and the percent error assuming the estimate in the first calculation to be correct. Use depths of: 1500 ft 5000 ft 15,000 ft The bulk modulus definition (equation 1.5.11 on page 17) is below. B = -for all dau p/dau for all = rho dau p/dau rho (at constant temperature T). Here for all is the volume.

Explanation / Answer

From the given data:

The pressure at different depts can be calculated by:

the stated bulk modulus formula.

As B = 310000 lb/in2

density = 2.0 slug/ ft3

and subsituting the values of depth h:

We get the pressure difference as

1) For h = 1500 ft

dp/dp = (310000+1500)/2 = 155.75 Kpa

2) For h = 5000 ft

dp/dp = (310000+5000)/2 = 157.50 Kpa

3) For h =15000 ft

dp/dp = (310000+15000)/2 = 162.50 Kpa

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