Liquids Physics principles of liquids

Density The density, ρ (rho), of an object is defined as the mass per unit volume ρ ≡ρ ≡ Units are grams/cm 3 or kg/m 3 The Specific Gravity of a substance is defined as: the ratio of the density of the substance to that of water at 4.0 o C (ρ H 2 O = 1.00g/cm 3 ). It has no units. SG ≡ (at 4 o C)

Specific Gravities Substance  SG  water1000 kg/m g/cm 3 1 mercury13600 kg/m g/cm air1.29 kg/m g/cm helium0.18 kg/m g/cm

Pressure in Liquids A liquid in a container exerts pressure on all surfaces of the container at once. The amount of the pressure depends on the depth of the liquid at that point… just as a taller block of wood exerts more pressure on a table than a shorter one. P = F/A = (F/A*depth) * depth  P = (F/volume) * depth  P = (weight density) * depth Is there more pressure at the bottom of a bathtub 30 cm deep or at the bottom of a pitcher of water 35 cm deep? There is the same amount of water in both containers to the right. Which one experiences greater pressure at the bottom?

Pressure in Liquids The deeper the object, the greater the pressure. Even an object floating exerts a force on the liquid and experiences pressure.

Archimedes and Buoyancy We all know that some objects float—that is, they are buoyed up by the pressure of the liquid they are submerged in. But why? When any object is submerged into any liquid it applies pressure to displace the liquid. According to Newton’s 3 rd law, what will the liquid do in response? There will be an equal and opposite reaction. Archimedes and the king’s crown… (earlier power-point) An object submerged displaces a volume of water the same as itself, of course Which means that the buoyant force will equal the weight of that water which was displaced or moved.

Buoyant force The deeper an object, the greater the pressure on it by the liquid. However, the difference between the upward and downward forces acting on a submerged object are the same regardless of the depth. The block weighs 7 lb in air and 4 lb in water… what is the buoyant force upon it?

To float or not to float… Why do some objects float in water and others sink? Why do ships, made out of heavy metals, float?! Applying this principle, what can we do to make our body float in a pool? Demo time!

Archimedes’ Principle Why do floaties or inner-tubes cause this child to float? Think in terms of Archimedes principle. They cause the child plus floatation device to occupy a greater volume, thus displacing more water.

Suppose you float a large ice-cube in a glass of water, and that after you place the ice in the glass the level of the water is at the very brim. When the ice melts, the level of the water in the glass will: 1. Go up, causing the water to spill out of the glass. 2. Go down. 3. Stay the same. Ice Cube Act

Boat Act Which weighs more: 1. A large bathtub filled to the brim with water. 2. A large bathtub filled to the brim with water with a battle-ship floating in it. 3. They will weigh the same. Would this be true if the ship did not float? Tub of water Tub of water + ship Overflowed water Why? No

Another Boat Act Does the lake water level go up or down when the anchor is tossed into the water? 1. The water level goes up. 2. The water level goes down. 3. The water level goes neither up nor down. Why?

Yet Another Boat Act A 200-ton ship enters the lock of a canal. The fit between the sides of the lock and the ship is tight so that the weight of the water left in the lock after it closes is much less than 200 tons. Can the ship still float if the quantity of water left in the lock is much less than the ship’s weight? Yes, as long as the water gets up to the ship’s waterline. No, the ship touches bottom because it weighs more than the water in the lock. The buoyant force doesn’t equal the weight of the object, but the weight of the water displaced. Why?

Specific Gravity Example Example: A rubber bar weighs 5.7 N in air. If the bar is completely submerged in water, its apparent weight is 4.6 N. Determine the specific gravity of the bar. (specific gravity = ρ bar /ρ water ) S.G. = F g / F B = 5.7N / (5.7N – 4.6N)  S.G. = 5.7N / 1.1N = 5.18 So we can also say that the bar has a density of 5.18 gm/cm 3 or 5180 kg/m 3

Another Density Example Example A block of wood floats on the surface of a lake with 60% of its volume below the surface of the water. What is the density of the wood? m =  V ⇒ mg =  Vg and since it’s floating mg = W wood = F B ⇒  wood V wood g =  water V disp g ⇒  wood V wood =  water V disp ⇒  wood =  water (V disp / V wood ) =  water (0.60)  wood = (10 3 kg/m 3 ) (0.60) = 600 kg/m 3 or 0.6 gm/cm 3

y faucet  P =  g(y water - y faucet ) = (10 3 kg/m 3 )(9.8 m/s 2 )(30m) = 2.94 x 10 5 Pa You go home, turn on the faucet, and water comes out. Why? y water

Air pressure varies with height and weather conditions. The “average” atmospheric pressure at sea level is defined as 1 atm. Atmospheric Pressure and Gauge Pressure It turns out that 1 atm = 1.013x10 5 N/m 2 = 101.3x10 3 Pa = kPa Also, 1 atm = 14.7 pounds/in 2 1 bar = 100 kPa (slightly less than 1 atm)

P tire air P atmosphere You use a tire gauge to measure tire pressure. It records 28 psi. Is that the actual pressure in the tire? You measure the pressure P G, which is the gauge pressure, or the difference between the absolute pressure and atmospheric pressure. Thus P = 28 psi psi = 42.7 psi is the actual pressure inside. OSE: P = P A + P G.

F 2 = ? fluid A1A1 A2A2 F1F1 P 1 = F 1 / A 1 P 2 = ? Pascal’s Principle Pressure applied to a enclosed fluid increases the pressure throughout by the same amount. Pressure is same throughout, so P 2 = F 2 /A 2 = P 1 = F 1 /A 1  F 1 /A 1 = F 2 /A 2 Thus F 2 = (A 2 / A 1 ) F 1.