Fluid Statics

The key concepts to learn in this chapter are pressure with depth in a static fluid and buoyancy. We begin with the definition of the density of a substance:

and the definition of pressure:

The air exerts a static pressure of 1.01 x 10⁵ N/m² (Pascals) all around us (click here for a discussion of this) due to its own weight; this pressure is also exerted within a container of water open to the atmosphere. At a depth of h = 10 meters in plain water, the pressure (acting in all directions at once) is a combination of the atmospheric pressure and the pressure of the water due to the weight of water above:

where

Using the information above, the extra fluid pressure (also called gauge pressure) is (1000 kg/m³)x(9.8 m/s²)x(10 m) = 0.98 x 10⁵ Pascals, which is about one atmosphere's worth of extra pressure.

The density of water is 1000 kg/m³, and serves as a standard for comparison. Water is much more dense than air, which is why a depth of only 10 m of water exerts a similar pressure on you compared to about 6 miles of air.

which turns out to be equal to the weight of the water that has been displaced by the object (the weight of an equivalent volume of water; a.k.a Archimede's Principle). This means that if the object immersed in the water is more dense than water, its weight will exceed this upward buoyant force and it will sink; and if the object immersed in the water is less dense than water, its weight will be less than this upward buoyant force and it will float.

• calculating the height that an IV bag has to be placed above the level of a needle for there to be infusion into the bloodstream.
• calculating the buoyant force acting on a submerged object or on a floating object; or determining if the described object will float or sink when placed in a fluid in a certain way.

• not using correct units to calculate gauge pressure or density. Convert depths to meters, pressures to Pascals, volumes to cubic meters, etc. before plugging into equations.
• not using given information in solving the problem. For example: I might tell you that the fluid is seawater or blood rather than water, so you should use the appropriate fluid density to calculate gauge pressure and/or buoyant force.
• forgetting that pressure and force are not the same thing. You have to multiply pressure by area over which it acts in order to get the force.
• forgetting that atmospheric pressure acts on both sides of any container wall (except where there is a partial or total vacuum). For infusion problems or problems involving leaking containers, flow is caused by any DP, which means that atmospheric pressure "cancels out" when you calculate the net force. But by the same token, you should know how to calculate the total pressure if I ask for that; then you would have to include P_atm.
• confusing the equation for the weight of a submerged object with the equation for buoyant force on that object. Often I will give you the density of the submerged object, from which you can calculate its weight using F_g = (r_obj)(V_obj)(g). You are then supposed to calculate the buoyant force and compare it with the weight, in order to show that the object floats or sinks. You can't use the object's density to calculate buoyant force; you need the density of the fluid instead.
• forgetting that the buoyant force on an object depends on how much of that object is immersed in a fluid. There is less buoyant force when it is only partially submerged.
• forgetting that the buoyant force on a totally-submerged object does not depend on the depth of fluid, or on what other forces might be acting on the object (such as normal force).

Click here for some test-level practice problems.

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