Suarden
A tank contains a pool of mercury 0.3 m deep, covered with a layer of water that is 1.2 m deep. The density of water is 1.0 x 10^3 kg/m3 and that of mercury is 13.6 x 10^3 kg/m3. Find the pressure exerted by the double layer of liquids at the bottom of the tank. Ignore the pressure of the atmosphere.

In a partially submerged but floating object example a boat on a lake, what is the magnitude of the buoyant force? Why would it have this value?

Gold Member
To solve this problem, assume the tank is one square meter at the base.

Then knowing the base and the height of each fluid, you can find the volume of each fluid.

Knowing the volume of each fluid and the density of each fluid, you can know the mass of each fluid.

Knowing the masses of both fluids, you can find the total weight of both fluids using the acceleration due to gravity.

The total weight will be the force on the bottom of the tank with a 1 square meter base. If the tank were twice as wide, the weight would be twuce as much.

The force per square meter, will be the pressure in pascals.

Also, the magnitude of the buoyant force is equal to the weight of the displaced fluid.

It has this value because of how the pressure of a fluid depends on the weight of the fluid above it.

The pressure at the bottom of the boat will be larger than the pressure closer to the surface, so that if you add up all the force due to the water pressure, you get a net force upwards. This is true no matter the shape of the boat.

mark.watson
Q1: The relationship between density and the specific weight of a fluid is γ = ρg, where γ is the specific weight, ρ is the density, and g is gravity. Next, the pressure-elevation relationship is
p = γh, where p is the pressure, γ is the specific weight, and h is the height of the fluid. For your question, just sum the pressures of each fluid.

Q2: The displaced fluid will exert a buoyant force that will exactly equal the weight of the floating object.

Gold Member
moreover, this law of buoyancy (force equals weight of displaced fluid) is true whether the surrounding fluid is compressible or incompressible, or whether the form of gravity you're using is local or universal.

vwmeche94
Ok gents, just to clarify... what is being said in a nutshell, and I'm going to use a basic example here... I have a tank 17'L x 8'D x 8'H and I fill to some height h1.

If I then introduce a solid body which displaces the fluid a height of 2', does my hydrostatic pressure (force) on the walls increase?

My thinking is that the force doesn't increase with adding the solid.

Staff Emeritus
Gold Member
Ok gents, just to clarify... what is being said in a nutshell, and I'm going to use a basic example here... I have a tank 17'L x 8'D x 8'H and I fill to some height h1.

If I then introduce a solid body which displaces the fluid a height of 2', does my hydrostatic pressure (force) on the walls increase?

My thinking is that the force doesn't increase with adding the solid.

We know that that pressure is given as P= ρgh. What is h before the solid is introduced? What is h after the solid is introduced? Has the pressure changed?

vwmeche94
Before the solid was introduced, the height was 6'. After the solid, height 7'-3", approximately.

vwmeche94 