Week 7 (Feb 24 - 28)

Read: Reason, Authority and Science (ASGv2 Chap. 13) and Pascal's Principle (ASGv2 Chap. 14).

Key topics: deductive and inductive reasoning, causality, final cause, hydrostatic paradox, pascal's principle, pressure.

PHY 201 Lecture: Fluid flow, torricelli's law; deriving a rate equation for draining a fluid-filled vessel.
Homework:
  1. Hydraulics: A fluid-filled syringe has a plunger with a diameter of 1 cm. The needle has a diameter of 1 mm. The plunger is depressed at a rate of 1 cm per second. (a) With what speed will the fluid squirt from the tip of the needle? (Answer: 100 cm/sec) (b) If the end of the needle is capped, and a force of 1 pound is applied to the plunger, what force will be applied to the end cap? (Answer: 1 / 100 pound)
  2. Fluid weight (Ex. 14.1)
  3. Fluid equilibrium and the center of gravity (Ex. 14.2a, b)

Lab: Pascal's principle and Torricelli's law (Ex. 14.5). We will be carrying out two lab experiments this week. In the first lab, we will be exploring pascal's principle by measuring the mechanical advantage of a hydraulic jack. In the second, we will be exploring Torricelli's law by measuring the flow rate of a draining water column.
  1. Pascal's principle lab: Set up a hydraulic jack. Before filling the jack with water, be sure you understand how it operates by using an air-filled jack to lift a heavy (1 or 2 kg) weight. Once you understand its operation, bleed the air from the system by filling it completely with water. Be sure that all of the air bubbles are removed from the chamber. Now, use a force sensor to measure the force that must be applied to a small diameter syringe in order to lift a known mass with the large diameter syringe in the body of the jack. Make a data table that includes the following: small syringe diameter and large syringe diameter, force applied to small syringe and force applied by large syringe, cross sectional area of small syringe and of large syringe, total distance moved by small syringe and by large syringe, actual mechanical advantage and ideal (theoretical) mechanical advantage, hydraulic jack efficiency. (Mechanical advantage is the ratio of the force-out over force-in. Efficiency Iis the ratio of work-out vs work-in.) Repeat this procedure for two different diameter small syringes. Finally answer the following questions: how efficient is your hydraulic jack? Are your results consistent with Pascal's principle? Is the work done by the small syringe equal to the work done by the large syringe?
  2. Torricelli's law (Ex. 14.5): Nearly fill your vertical column with water by plugging the horizontal exit nozzle at the bottom. Set up a horizontal ruler by the exit nozzle near the bottom of the column. Also, set up a camera so that you can record the water stream as it leaves the nozzle. When everything is ready, remove the nozzle and record the water draining from the exit nozzle. You will need to simultaneously record the height of the water level (above the nozzle) as a function of time as the column drains through the nozzle. Now, from any individual frame of your movie, you should be able to calculate the ``muzzle velocity" of the water as it squirts from the nozzle. Hint: you can calculate the muzzle velocity from the range and the height of the nozzle, just like in your (previous) projectile motion lab. Once you have a large number of your movie frames analyzed, you will need to correlate the muzzle velocity with the water level. Plot velocity versus water level. Does your data agree with Torricelli's law? Try a power law fit to your data. Does it work? Notice that the fluid flow may in fact stop before the column height is exactly zero; this is due surface tension: a meniscus forms at the output nozzle that can support a small column of fluid. So you may need to incorporate an offset into your power-law fitting function to account for this. If you are a PHY 201 student, you should also calculate (by integrating the continuity equation) how much time it should take for your column to completely drain. Do your calculations match your measured drainage time?

Chapter 13 (1 video):



Chapter 14 (11 videos):






















Physics 1