1、Fluid Mechanics - Hydrostatics,AP Physics B,States of Matter,Before we begin to understand the nature of a Fluid we must understand the nature of all the states of matter: The 3 primary states of matter - solid - Definite shape and volume. - liquid -Takes the shape of its container, yet has a defini

2、te volume. - gas - Takes the shape and volume of its container. Special states - Plasma, Bose-Einstein Condensate,Density,The 3 primary states have a distinct density, which is defined as mass per unit of volume.,Density is represented by the Greek letter, “RHO”, r,What is a Fluid?,By definition, a

3、fluid is any material that is unable to withstand a static shear stress. Unlike an elastic solid which responds to a shear stress with a recoverable deformation, a fluid responds with an irrecoverable flow. Examples of fluids include gases and liquids.,Why fluids are useful in physics?,Typically, li

4、quids are considered to be incompressible. That is once you place a liquid in a sealed container you can DO WORK on the FLUID as if it were an object. The PRESSURE you apply is transmitted throughout the liquid and over the entire length of the fluid itself.,Pressure,One of most important applicatio

5、ns of a fluid is its pressure- defined as a Force per unit Area,Example,A water bed is 2.0 m on a side an 30.0 cm deep. (a) Find its weight if the density of water is 1000 kg/m3. (b) Find the pressure the that the water bed exerts on the floor. Assume that the entire lower surface of the bed makes c

6、ontact with the floor.,1.2 m3,1200 kg,11760 N,2940 N/m2,Hydrostatic Pressure,Suppose a Fluid (such as a liquid) is at REST, we call this HYDROSTATIC PRESSURE Two important points A fluid will exert a pressure in all directions A fluid will exert a pressure perpendicular to any surface it compacts,No

7、tice that the arrows on TOP of the objects are smaller than at the BOTTOM. This is because pressure is greatly affected by the DEPTH of the object. Since the bottom of each object is deeper than the top the pressure is greater at the bottom.,Pressure vs. Depth,Suppose we had an object submerged in w

8、ater with the top part touching the atmosphere. If we were to draw an FBD for this object we would have three forces The weight of the object The force of the atmosphere pressing down The force of the water pressing up,mg,Fatm,Fwater,Fwater= Fatm + mg,Pressure vs. Depth,But recall, pressure is force

9、 per unit area. So if we solve for force we can insert our new equation in.,Note: The initial pressure in this case is atmospheric pressure, which is a CONSTANT. Po=1x105 N/m2,A closer look at Pressure vs. Depth,ABSOLUTE PRESSURE,Initial Pressure May or MAY NOT be atmospheric pressure,Depth below su

10、rface,Gauge Pressure = CHANGE in pressure or the DIFFERENCE in the initial and absolute pressure,Example,a) Calculate the absolute pressure at an ocean depth of 1000 m. Assume that the density of water is 1000 kg/m3 and that Po= 1.01 x 105 Pa (N/m2). b) Calculate the total force exerted on the outsi

11、de of a 30.0 cm diameter circular submarine window at this depth.,9.9x106 N/m2,2.80 x 106 N,A closed system,If you take a liquid and place it in a system that is CLOSED like plumbing for example or a cars brake line, the PRESSURE is the same everywhere. Since this is true, if you apply a force at on

12、e part of the system the pressure is the same at the other end of the system. The force, on the other hand MAY or MAY NOT equal the initial force applied. It depends on the AREA. You can take advantage of the fact that the pressure is the same in a closed system as it has MANY applications. The idea

13、 behind this is called PASCALS PRINCIPLE,Pascals Principle,Another Example - Brakes,In the case of a cars brake pads, you have a small initial force applied by you on the brake pedal. This transfers via a brake line, which had a small cylindrical area. The brake fluid then enters a chamber with more

14、 AREA allowing a LARGE FORCE to be applied on the brake shoes, which in turn slow the car down.,Buoyancy,When an object is immersed in a fluid, such as a liquid, it is buoyed UPWARD by a force called the BUOYANT FORCE.,When the object is placed in fluid is DISPLACES a certain amount of fluid. If the

15、 object is completely submerged, the VOLUME of the OBJECT is EQUAL to the VOLUME of FLUID it displaces.,Archimedess Principle, An object is buoyed up by a force equal to the weight of the fluid displaced.,In the figure, we see that the difference between the weight in AIR and the weight in WATER is

16、3 lbs. This is the buoyant force that acts upward to cancel out part of the force. If you were to weight the water displaced it also would weigh 3 lbs.,Archimedess Principle,Example,A bargain hunter purchases a gold crown at a flea market. After she gets home, she hangs it from a scale and finds its weight in air to be 7.84 N. She then weighs the c