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CHAPTER 10 HYDROSTATIC AND HYDRAULIC MACHINES CHAPTER LEARNING OBJECTIVES Upon completion of this chapter, you will be able to do the following:
In this chapter we will discuss briefly the pressure of liquids: (1) hydrostatic (liquids at rest) and (2) hydraulic (liquids in motion). We will discuss the operation of hydrostatic and hydraulic machines and give applications for both types. HYDROSTATIC PRESSURE You know that liquids exert pressure. The pressure exerted by seawater, or by any liquid at rest, is known as hydrostatic pressure. If you are billeted on a submarine, you are more conscious of the hydrostatic pressure of seawater. When submerged, your submarine is squeezed from all sides by this pressure. A deepsea diving submarine must be able to withstand the terrific force of water at great depths. Therefore, the air pressure within it must be equal to the hydrostatic pressure surrounding it. PRINCIPLES OF HYDROSTATIC PRESSURE In chapter 9 you found out that all fluids exert pressure in all directions. That’s simple enough. How great is the pressure? Try a little experiment. Place a pile of blocks in front of you on the table. Stick the tip of your finger under the first block from the top. Not much pressure on your finger, is there? Stick it between the third and fourth blocks. The pressure on your finger has increased. Now slide your finger under the bottom block in the pile. There you will find the pressure is greatest. The pressure increases as you go lower in the pile. You might say that pressure increases with depth. The same is true in liquids. The deeper you go, the greater the pressure becomes. However, depth isn’t the whole story. Suppose the blocks in the preceding paragraph were made of lead. The pressure at any level in the pile would be considerably greater. Or suppose they were blocks of balsa woodthen the pressure at each level wouldn’t be as great. Pressure, then, depends not only on the depth, but also on the weight of the material. Since you are dealing with pressure—force per unit of area, you will also be dealing with weight per unit of volumeor density. When you talk about the density of a substance, you are talking about its weight per cubic foot or per cubic inch. For example, the density of water is 62.5 pounds per cubic foot; the density of lead is 710 pounds per cubic foot. However, to say that lead is heavier than water isn’t a true statement. For instance, a 22caliber bullet is the same density as a pail of water, but the pail of water is much heavier. It is true, however, that a cubic foot of lead is much heavier than a cubic foot of water. Pressure depends on two principlesdepth and density. You can easily find the pressure at any depth in any liquid by using the following formula: P= H x D in which P = pressure, in lb per sq in. or lb per sq ft H = depth of the point, measured in feet or inches and D = density in lb per cu in. or lb per cu ft Note: If you use inches in your computation, you must use them throughout; if you use feet, you must use them throughout. What is the pressure on 1 square foot of the surface of a submarine if the submarine is 200 feet below the surface? Using the formula: P= H x D P= 200 x 62.5 = 12,500 lb per sq ft Every square foot of the sub’s surface that is at that depth has a force of more than 6 tons pushing in on it. If the height of the hull is 20 feet and the area in question is between the sub’s top and bottom, you can see that the pressure on the hull will be at least (200 – 10) x 62.5 = 11,875 pounds per square foot. The greatest pressure will be (200 + 10) x 62.5= 13,125 pounds per square foot. Obviously, the hull has to be very strong to withstand such pressures. 

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