Change in density of water

[Abhishekdas]

Change in density of water...

Homework Statement

Calculate the approximate change in density of water in a lake at a depth of 400m below the surface. The density of water at the surface is 1030kg/m³ and bulk modulus(B) of water is 2*10⁹...

Homework Equations

rho=rho₀(1/(1-dP/B))
rho = density of water at any depth
rho₀ = density of water at surface
dP= change in pressure

The Attempt at a Solution

How to calculate dP if i use h*rho*g , rho is not constant...So how do i go about it...Please help...

 

[amy andrews]

I only know how to approximate this without calculus...it gets very,very close to the real value anyway.
First, assume that the density remains constant, and find the pressure at 400m using that density. Then recalculate the second density using that pressure.
Hope this helps!

 

[Abhishekdas]

Ok...thanks i will try it...
I am sorry i didnt notice your reply for a long time...

 

[Abhishekdas]

my answer is 2.12618 and answer in the book is 2...I guess they are expecting this answer ...But you it should be close as we are dealing with values of pressure musch lesser than Bulk modulus of water...But this is'nt a correct method is'nt it? Neway...thanks a lot for your help...

 

[rwisz]

To calculate the change in density of water at a depth of 400m, we can use the equation:

dP = h * rho * g

Where:
dP = change in pressure
h = depth (400m in this case)
rho = density of water at that depth (unknown)
g = gravitational acceleration (9.8m/s^2)

We can rearrange the equation to solve for rho:

rho = dP / (h * g)

Now, to calculate the change in pressure (dP), we can use the bulk modulus of water (B) and the initial density of water at the surface (rh in the equation:

dP = B * (rho - rh

Substituting the given values, we get:

dP = (2*10^9) * (rho - 1030)

Now, we can plug this into our previous equation to solve for rho:

rho = [(2*10^9) * (rho - 1030)] / (400 * 9.8)

Solving for rho, we get an approximate value of 1030.2 kg/m^3.

Therefore, the change in density of water at a depth of 400m is approximately 0.2 kg/m^3.

It is important to note that this is only an approximate calculation, as the density of water can vary at different depths due to factors such as temperature and salinity. Further analysis and measurements would be needed to determine the exact change in density at this depth.