# Estimate the density of the water

## Homework Statement

Estimate the density of the water 5.7 km deep in the sea. (bulk modulus for water is B=2.0 x 10^9 N/m^2) By what fraction does it differ from the density at the surface?

## Homework Equations

P=(rho)gh=F/A=B(delta l/l)

## The Attempt at a Solution

So I have several equations above. I wanted so solve for rho using the first equation but I don't know pressure. I tried the second equations but I don't know Force or area. I tried the last equation but I would need delta l and l so basically I'm stuck. Some advice would be much appreciated.

LowlyPion
Homework Helper
Estimate the density of the water 5.7 km deep in the sea. (bulk modulus for water is B=2.0 x 10^9 N/m^2) By what fraction does it differ from the density at the surface?

## Homework Equations

P=(rho)gh=F/A=B(delta l/l)

## The Attempt at a Solution

So I have several equations above. I wanted so solve for rho using the first equation but I don't know pressure. I tried the second equations but I don't know Force or area. I tried the last equation but I would need delta l and l so basically I'm stuck. Some advice would be much appreciated.

Well they do say estimate. So maybe try to work it out assuming that p doesn't change?

(Yes it changes, but does it change enough to matter? See what results you get and then decide.)

Well they do say estimate. So maybe try to work it out assuming that p doesn't change?

(Yes it changes, but does it change enough to matter? See what results you get and then decide.)

I don't understand. I'm suppose to be solving for p at a certain density. How can it not change?

LowlyPion
Homework Helper
I don't understand. I'm suppose to be solving for p at a certain density. How can it not change?

Have you calculated it using a uniform p as to the effect it will have on a bulk modulus of 2 * 109?

In 6 km, the change in pressure is significant.

Here's something to get you started:

Use the equation,

B=dP/(d(rho)/rho)

Manipulate and integrate,

integral of (d(rho)/rho) = integral of (dP/B)

That results in,

ln(rho2/rho1)=exp((P2-P1)/B)

Where you can say state 1 is the surface, and state 2 is the state at 5.7 km down.

You can then use the rho*g*h equation.