This recitation will focus on properties of fluides inclucing Pascal's Principle, Archimedes' Principle, and the Equation of Continuity. Please experiment with the Physlet simulations below and complete the required calculations on your worksheet.
The physlet above displays a toy model of a hydraulic lift commonly found in auto repair shops. Hydraulic systesms are governed by Pascal's principle which states that "an external pressure applied to an enclosed fluid is transmitted unchanged to every point within the fluid". Thus, the pressure at the surface of the small piston must be the same as the pressure at the surface of the large piston. Both pistons are rectanguler with the smaller having sides of length 4 cm and the larger having sides of lengths 13 cm. You can control the applied force and the distance with which the force moves the smaller piston.
The physlet above simulate a blood corpuscle traveling through a narrowing in an artery. The artery is assumed to have a circular cross-section. The continuity equation states that v1A1 = v2A2. Thus, the velocity of the corpuscle should be higher in the narrowing where the area is smaller. The artery initially has a diameter of 6 cm which yields a cross section of 28.3 cm2 and the corpuscle moves at 18 cm/s.
The physlet above simulates the lowering of a mass into a beaker of water. The spring scale indicates the force necessary to support the mass. This force will be less when the mass is submerged in the water due to Archimedes' Principle. This can be stated as "an object completely immersed in a fluid experiences an upward buoyant force equal in magnitude to the weight of fluid displaced by the object". This is really a manifestation of the fact that pressure increases with depth. Thus, the pressure acting on the bottom of a submered mass is greater than that acting on the top of the mass. We can use this information to calculate the density and the volume of the mass. These tricks have been used by metalurgists to determine the purity of precious metals since the time of Archimedes.
Our two equations are:
We can solve for the density of the mass by using the first equation to eliminate volume from the second equation.
We can now subsitute this value of density back into the first equation to solve for volume.
