Hydrostatics Fluids at Rest

Objectives Define and apply the concepts of density and fluid pressure to solve physical problems. Define and apply concepts of absolute, gauge, and atmospheric pressures. State Pascal’s law and apply for input and output pressures. State and apply Archimedes’ Principle to solve physical problems. Tell students to come back to this later!

What is a Fluid? Fluids have a definite volume… Gases do not

Density vs. Mass Density What is Density? density is a measure of a quantity of a substance in a given space How is it different than Mass Density? mass density measures the mass of a substance in a given space ~ we will use this!

Common Density’s Mention the symbol for density

Steel (7800 kg/m3) rr = 7.80 Brass (8700 kg/m3) rr = 8.70 Specific Gravity The specific gravity rr of a material is the ratio of its density to the density of water (1000 kg/m3). No Units! Why would know specific gravity of a substance be a useful measurement? Steel (7800 kg/m3) rr = 7.80 Brass (8700 kg/m3) rr = 8.70 Wood (500 kg/m3) rr = 0.500

Question Six objects (A-F) are in a liquid, as shown. None of them are moving. Arrange them in order of density, from lowest to highest.

Answer Full answer to the question: B, D, A, F, E, C. The more of an object's volume is above the water surface, the less dense it is. Object B must therefore be the least dense, followed by D, A, and F. Object E is next, because it is neutrally buoyant and equal in density to the liquid. Object C is negatively buoyant because it is more dense than the fluid.

Question: Why do things feel lighter in water than they do in air? ANSWER: The reason is that a fluid exerts an upward force on objects that are partially or completely submerged in it. This upward force is called a buoyant force. The reason is that a fluid exerts an upward force on objects that are partially or completely submerged in it. This upward force is called a buoyant force.

Buoyant Force Acts in the opposite Direction of the Force of gravity Net force acting on an object is therefore ALWAYS smaller than zero The weight of an object in water is it’s apparent weight If the objects Specific Gravity is less than 1, the buoyant force is larger than gravity and therefore an object floats!

Archimedes Principle Any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object.

Confusing! Focus on misconception: DENSITY OF FLUID NOT SUBSTANCE

Sinking vs. Floating

Question A cube of steel that measures 5.0 cm on each side is immersed in water. The density of steel is 9.0 x 103 kg/m3. The density of water is 1.0 x 103 kg/m3. What is the…. buoyant force acting on the cube? and… its apparent weight?

Answer: (a) Find the buoyant force. The volume of the cube is:   (b) Find the apparent weight. The weight of the cube is: Now we can plug and chug: To find the apparent weight we use this equation:

Extra Questions: A 2.8 kg rectangular air mattress is 2.00 m long, 0.500 m wide, and 0.100 m thick. What mass can it support in water before sinking? A ferry boat is 4.0 m wide and 6.0 m long. When a truck pulls onto it, the boat sinks 4.00 cm in the water. What is the weight of the truck? An empty rubber balloon has a mass of 0.0120 kg. The balloon is filled with helium at 0°C, 1 atm pressure, and a density of 0.179 kg/m3. The filled balloon has a radius of 0.500 m. What is the magnitude of the buoyant force acting on the balloon? (Hint: See Table 1 for the density of air.) What is the magnitude of the net force acting on the balloon?

Answers 97kg 9.4×103N a. 6.63 N b. 5.59 N

Pressure What is pressure? Pressure is a measure of how much force is applied over a given area.

Pascal’s Principal/Pascal’s Law Pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of the container.

Hydraulic Lift The key: Pressure is equal at both points of the lift

Question The small piston of a hydraulic lift has an area of 0.20 m2. A car weighing 1.20 x 104 N sits on a rack mounted on the large piston. The large piston has an area of 0.90 m2. How large a force must be applied to the small piston to support the car? ANS: F1 = 2.7 x 103 N

Depth Why are submarine hulls made of thick layers of titanium or steel? Pressure in fluids increases with depth! We can derive this from our pressure formula. Gauge Pressure:

Fluid Pressure as a function of depth Atmospheric Pressure: P0 = 1.0 x 105 Pa

Connecting Buoyant Force to Pressure Explain why the force at the bottom of the object is greater than at the top of the object. ANS: at greater depth the pressure is great resulting in a great force on the bottom than the top

ΔP = 196 kPa ΔP = 296 kPa Question 1: ρ = 1000 kg/m3 h ρ = 1000 kg/m3 A diver is located 20 m below the surface of a lake (ρ = 1000 kg/m3). What is the gauge pressure due to the water? What is the absolute pressure? ΔP = 196 kPa ΔP = 296 kPa

Question 2: A 2-kg brass block is attached to a string and submerged underwater. Find the buoyant force and the tension in the rope. Include a Force diagram! Density = 8700 kg/m3 FB + T = mg FB = ρwgVw mg FB = rgV T Force diagram FB = 2.25 N T = 17.3 N