Question dealing with density and pressure

[tophat22]

I haven't taken physics in a while, and most of this is physics related. My professor's lectures have not helped me understand the material, so I have questions on my homework. I would like to learn how to approach this problem and solve it.


The figure shows a vertical dam holding back a reservoir of depth h. The lower half of the reservoir consists of a sludge whose density is twice that of water, and the upper half of the reservoir's volume consists of pure water.

a. Determine how pressure depends on altitude z in the water and sludge.
b. Let w be the dam's width, and determine the horizontal component of force on the dam.


Thank you in advance.

 

[tiny-tim]

Welcome to PF!

Hi tophat22! Welcome to PF!

The figure shows a vertical dam holding back a reservoir of depth h. The lower half of the reservoir consists of a sludge whose density is twice that of water, and the upper half of the reservoir's volume consists of pure water.

a. Determine how pressure depends on altitude z in the water and sludge.
b. Let w be the dam's width, and determine the horizontal component of force on the dam.

a. The pressure is basically the weight of the fluid above (per area).

b. Pressure = force per area, so the force on the dam is the integral of pressure times area.

 

[tophat22]

for part a, what am I supposed to do with vector z? will I have to deal with an integral?

 

[tiny-tim]

Hi tophat22!

for part a, what am I supposed to do with vector z? will I have to deal with an integral?

No, you'd only need an integral if the density was varying continuously …

but here, it's constant to a certain height, and then a different constant, so you can just multiply instead of integrating.

 

[stewartcs]

Hi tophat22!


No, you'd only need an integral if the density was varying continuously …

but here, it's constant to a certain height, and then a different constant, so you can just multiply instead of integrating.

Since the pressure varies with depth there will be a different force on the dam at different depths. So integration would be needed.

CS

 

[tiny-tim]

for part a, what am I supposed to do with vector z? will I have to deal with an integral?

Since the pressure varies with depth there will be a different force on the dam at different depths. So integration would be needed.

CS

Hi stewartcs!

Not for part a.

 

[stewartcs]

Hi stewartcs!

Not for part a.

Sorry I missed the "part a" there! Silly me...I should not post until my morning tea!

CS

 

[tiny-tim]

It's afternoon here in London!

'll soon be proper tea-time

… and time for "Countdown" on telly. ​