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1 Name Partner Date Class FLUIDS Part 1: Archimedes' Principle Equipment: Dial-O-Gram balance, small beaker ( ml), metal specimen, string, calipers. Object: To find the density of an object using Archimedes' Principle. Method: Using distilled water, a beaker and Dial-O-Gram balance, determine the volume and density of one of the metal specimens. Use the arrangement depicted in Figure 1. You must first weigh the sample in air (ignore the buoyant force of air) and then submerge the sample in water and weigh it again, the difference is the buoyant mass which is equal to the mass of the displaced fluid. These two measurements (and the fluid density) are all that's required to find the volume and density of the object. (Note: Ignore any volume markings on the beaker and use the buoyant force principle). If you are unsure of Archimedes' principle see your text. Fill in the table below by using the experimental setup shown in Figure 1. air fluid Buoyant mass Volume of fluid displaced Figure 1 Determine the geometrical volume of the specimen. State your method of measurement, equipment used, and show your work below. Compare this with the volume estimated using Archimedes' principle. (% error) Compare the calculated density of your specimen to that listed in a standard density table for the particular material of the specimen. (% error) 1

2 Part 1B. Use the specimen that you used in the previous section to find the density of the unknown fluid. Hint: You should, by this time, know the volume of the specimen. Use the specimen volume that you determined by Archimedes' principle. Make sure that you show all of your data and calculations. air fluid Buoyant mass Density of fluid Determine the density of your unknown fluid by measuring the mass of a 100 ml volume of the fluid. Compare this to the density calculated using Archimedes Principle using percent difference. Part 1C. Use Archimedes' Principle to calculate the minimum mass necessary to sink a small plastic boat. Show all of your work below. Measure the boat's mass and determine the amount of mass that you will add to just sink the boat. Perform the experiment and compare the calculated payload with the experimental payload that just sank the boat. Make sure that you show all of your data and calculations. Questions: Show your work. 1. A barge is shaped like an open box, 12 m wide by 30 m long and 6 m in the vertical dimension. The barge has a mass of 100,000 kg. How heavy a payload, in kg, can the barge carry if the maximum draft is to be 2 m? Draft is the amount below water level. 2

3 Part 2: Reading a manometer to find the absolute pressure in a flask. Equipment: manometer (a U tube with liquid in the bottom) (don't touch), barometer (on wall in SE corner of Lab) There is a flask in the lab which is connected to one side of a manometer; the other side is open to the atmosphere. Imagine a disk perpendicular to the axis of the manometer tube and located at the bottom of the U. What would happen to such a disk if the pressure on one side were greater than the pressure on the other? Now think about the pressures on each side of the manometer. On the flask side, there is the pressure in the flask and the pressure due to the column of liquid on that side of the manometer. Show that the pressure (Force/area) exerted by a column of liquid with density ρ is ρgh. So the total pressure on the flask side of the barometer is P 1 = P (flask) + The total pressure on the other side of the manometer, which is open to the atmosphere, is P 2 = P (atm) + weight Vg P area A Now, remember our imaginary disk at the bottom of the manometer. The liquid in the manometer is not moving (or wait until it isn t), so neither would such a disk be moving. Use this to relate the pressures on each side as calculated above. Subtract out any common factors to get your final relation, given below. (Show your work) P (flask) = P (atm) + gh Determine the absolute pressure (pressure above absolute vacuum) in the flask in Torr, mm Hg, dynes/cm 2, atmospheres and pounds/in 2. HINT: You will have to read the barometer in lab to do this since you will need atmospheric pressure. 1 atm = 760 Torr = 760 mmhg = x 10 5 N m 2 =1.013 x dynes 106 cm lbs / in2 1 Pa = 1 N/m Pa = 1 hpa (from our weird barometer; 1hPa = 1millibar, which is a common unit used in meteorology.) 3

4 How is pressure measured in mmhg? It used to be common to use mercury in manometers and barometers because of its high density. One atmosphere of pressure pushed up a column of 760 mm of mercury. Torricelli made a mercury barometer to measure the atmospheric pressure by sealing off one side of a manometer and filling the entire manometer with mercury (no air space on the sealed side). A simpler modification of this, which he used, was to fill a long tube sealed at one end with mercury and then invert it in a dish of mercury open to the atmosphere. Note that both of these instruments naturally measure pressure in units of mm Hg. One can measure the gauge pressure, in mm Hg, by taking the difference in height of a manometer with mercury as the liquid column. (P = gh; the value for h, in mm, is the number reported; mercury specifies the value for as 13.6 g/cm 3 which, along with the value for the gravitational acceleration, g, would be involved in calculating actual pressure units in Pa or N/m 2.) Questions: Show your work. 2. Given the following drawing of a manometer find the gauge pressure and absolute pressure in the container in Pascals and pound/in 2. The liquid used is alcohol of density 624 kg/m 3. The barometric pressure is 755 mm Hg. 3. Is the gauge pressure positive or negative in problem # 2? 4. is the absolute pressure positive or negative in problem #2? Is it possible to have a negative absolute pressure? Discuss: 4

5 Torricelli's equation (a special case of Bernoulli's Principle). Evangelista Torricelli ( ) first proposed the relationship below. The speed that a non-viscous fluid will exit a hole which is a distance h below the water level is v 2gh Refer to this as the theoretical velocity of the water leaving the tank. Use a 2-liter soda bottle with hole in the side to check this relationship for three different water levels, h. Set the bottle on the edge of the sink and allow the water to squirt out into the sink. Put three marks on the side and measure x as the water level drops to each of these marks. h y Starting with x=vt and y=1/2gt 2 for a projectile launched horizontally from a distance y above the ground derive the experimental velocity formula x v 2y g Show all steps to your derivation. X Make a graph showing the exit velocity versus height h (water level above the hole). Plot both experimental and theoretical values of v on this graph. How do your experimental values of velocity compare to the theoretical values? (Are they always higher, always lower, or randomly scattered about the theoretical values?) Give at least two reason(s) explaining why you think that your experimental values compare to the theoretical values as they do. Make sure your reasoning is consistent with your experimental results and think about effects considered and assumptions made in the theoretical calculation. 5