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# Fluid pressure problems and solutions

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Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Analysis The pressure relative to the atmospheric pressure is called the gage pressure, and the pressure relative to an absolute vacuum is called absolute pressure.

Discussion Most pressure gages like your bicycle tire gage read relative to atmospheric pressure, and therefore read the gage pressure. Analysis Atmospheric air pressure which is the external pressure exerted on the skin decreases with increasing elevation.

Therefore, the pressure is lower at higher elevations. As a result, the difference between the blood pressure in the veins and the air pressure outside increases.

This pressure imbalance may cause some thin-walled veins such as the ones in the nose to burst, causing bleeding. The shortness of breath is caused by the lower air density at higher elevations, and thus lower amount of oxygen per unit volume. Discussion People who climb high mountains like Mt. Everest suffer other physical problems due to the low pressure.If you limp into a gas station with a nearly flat tire, you will notice the tire gauge on the airline reads nearly zero when you begin to fill it.

In fact, if there were a gaping hole in your tire, the gauge would read zero, even though atmospheric pressure exists in the tire. Why does the gauge read zero? There is no mystery here. Tire gauges are simply designed to read zero at atmospheric pressure and positive when pressure is greater than atmospheric.

Similarly, atmospheric pressure adds to blood pressure in every part of the circulatory system. But atmospheric pressure has no net effect on blood flow since it adds to the pressure coming out of the heart and going back into it, too. What is important is how much greater blood pressure is than atmospheric pressure. Blood pressure measurements, like tire pressures, are thus made relative to atmospheric pressure.

In brief, it is very common for pressure gauges to ignore atmospheric pressure—that is, to read zero at atmospheric pressure. We therefore define gauge pressure to be the pressure relative to atmospheric pressure. Gauge pressure is positive for pressures above atmospheric pressure, and negative for pressures below it.

Hydrostatic Forces on Surfaces Problem 5

Gauge pressure is the pressure relative to atmospheric pressure. In fact, atmospheric pressure does add to the pressure in any fluid not enclosed in a rigid container. The total pressure, or absolute pressureis thus the sum of gauge pressure and atmospheric pressure:.

For example, if your tire gauge reads 34 psi pounds per square inchthen the absolute pressure is 34 psi plus For reasons we will explore later, in most cases the absolute pressure in fluids cannot be negative. Fluids push rather than pull, so the smallest absolute pressure is zero. A negative absolute pressure is a pull. There are a host of devices for measuring pressure, ranging from tire gauges to blood pressure cuffs. The undiminished transmission of pressure through a fluid allows precise remote sensing of pressures.

Figure shows one of the many types of mechanical pressure gauges in use today. In all mechanical pressure gauges, pressure results in a force that is converted or transduced into some type of readout. Consider the U-shaped tube shown in Figurefor example.A fluid is a substance that flows easily.

Gases and liquids are fluids, although sometimes the dividing line between liquids and solids is not always clear. Because of their ability to flow, fluids can exert buoyant forces, multiply forces in a hydraulic systems, allow aircraft to fly and ships to float. The topic that this page will explore will be pressure and depth.

If a fluid is within a container then the depth of an object placed in that fluid can be measured. The deeper the object is placed in the fluid, the more pressure it experiences. This is because is the weight of the fluid above it.

The more dense the fluid above it, the more pressure is exerted on the object that is submerged, due to the weight of the fluid. The formula that gives the P pressure on an object submerged in a fluid is:.

If the container is open to the atmosphere above, the added pressure must be included if one is to find the total pressure on an object. The total pressure is the same as absolute pressure on pressure gauges readings, while the gauge pressure is the same as the fluid pressure alone, not including atmospheric pressure.

A Pascal is the unit of pressure in the metric system. Example: Find the pressure on a scuba diver when she is 12 meters below the surface of the ocean. Assume standard atmospheric conditions. Solution: The density of sea water is 1. Fairman - August A fluid is a substance that flows easily. The density of water is 1. Find the total force exerted on a 20 cm by 20 cm square window. Use the density of sea water given above. What is the pressure difference between the upper and lower surfaces of its wing? Express your answer in atmospheres.Pressure is defined for all states of matter, but it is particularly important when discussing fluids.

### Pressure, Speed, and Bernoulli’s Equation in Physics Problems

An important characteristic of fluids is that there is no significant resistance to the component of a force applied parallel to the surface of a fluid. The molecules of the fluid simply flow to accommodate the horizontal force. A force applied perpendicular to the surface compresses or expands the fluid. If you try to compress a fluid, you find that a reaction force develops at each point inside the fluid in the outward direction, balancing the force applied on the molecules at the boundary.

The pressure at the bottom of the container is due to the pressure of the atmosphere p 0 plus the pressure due to the weight of the fluid. The pressure due to the fluid is equal to the weight of the fluid divided by the area. The weight of the fluid is equal to its mass times the acceleration due to gravity. The pressure at the bottom of the container is therefore equal to atmospheric pressure added to the weight of the fluid divided by the area:.

The pressure at a depth in a fluid of constant density is equal to the pressure of the atmosphere plus the pressure due to the weight of the fluid, or. Suppose the dam is m wide and the water is The average pressure p due to the weight of the water is the pressure at the average depth h of Although this force seems large, it is small compared with the 1.

In fact, it is only 0. A static fluid is a fluid that is not in motion. At any point within a static fluid, the pressure on all sides must be equal—otherwise, the fluid at that point would react to a net force and accelerate. The pressure at any point in a static fluid depends only on the depth at that point.

As discussed, pressure in a fluid near Earth varies with depth due to the weight of fluid above a particular level.

In the above examples, we assumed density to be constant and the average density of the fluid to be a good representation of the density. This is a reasonable approximation for liquids like water, where large forces are required to compress the liquid or change the volume. In a swimming pool, for example, the density is approximately constant, and the water at the bottom is compressed very little by the weight of the water on top.

Traveling up in the atmosphere is quite a different situation, however. Fluid located at deeper levels is subjected to more force than fluid nearer to the surface due to the weight of the fluid above it. Therefore, the pressure calculated at a given depth is different than the pressure calculated using a constant density. The weight of the element itself is also shown in the free-body diagram. Using a Cartesian y-axis oriented up, we find the following equation for the y-component:.

Note that if the element had a non-zero y-component of acceleration, the right-hand side would not be zero but would instead be the mass times the y-acceleration. The mass of the element can be written in terms of the density of the fluid and the volume of the elements:. This equation tells us that the rate of change of pressure in a fluid is proportional to the density of the fluid.

If the range of the depth being analyzed is not too great, we can assume the density to be constant. But if the range of depth is large enough for the density to vary appreciably, such as in the case of the atmosphere, there is significant change in density with depth. In that case, we cannot use the approximation of a constant density. Note that the pressure in a fluid depends only on the depth from the surface and not on the shape of the container.

The change in atmospheric pressure with height is of particular interest. Assuming the temperature of air to be constant, and that the ideal gas law of thermodynamics describes the atmosphere to a good approximation, we can find the variation of atmospheric pressure with height, when the temperature is constant.

We discuss the ideal gas law in a later chapter, but we assume you have some familiarity with it from high school and chemistry. Let p y be the atmospheric pressure at height y. Using density from the ideal gas law, the rate of variation of pressure with height is given as.The surface area of fish pressed by the water above it is 6 cm 2. Determine the force of water above fish that acts on fish.

Known :. Wanted : Force of the water above fish that acts on fish. Solution :. Equation of pressure :. The normal pressure of blood is 80 mm hg to mm hg. This value is equal to… Advertisement Advertisement. Wanted: This value is equal to… Pascal.

The correct answer is D. Above the surface of the sea, the height of mercury in a barometer is mm. If at a place, the height of mercury in a barometer is mm. Determine the pressure of air at that place. Wanted: Determine the pressure of air if the height of mercury is mm. The distance between the two troughs of the water surface waves is 20 m.

An object floats on the surface of The tension force of the rope is An object vibrates with a frequency of 5 Hz to rightward and leftward. The object moves from equilibrium point to the Pressure of fluids — problems and solutions 1. Known : Acceleration due to gravity Advertisement. Related Posts Force of gravity and gravitational field — problems and solutions 1.

Two objects m1 and m2 each with a mass of 6 kg and 9 kg separated by a distance of Parabolic motion, work and kinetic energy, linear momentum, linear and angular motion — problems and solutions 1.

Transverse waves — problems and solutions 1. Speed of the mechanical waves — problems and solutions 1. Simple harmonic motion — problems and solutions 1. By continuing to use the site, you agree to the use of cookies.Hydraulic systems are part of the fluid power industry. These systems will use hydraulic fluids to create pressure. At present, hydraulics is an area for research and the growth is visible for us. Almost every industry utilize some applications of hydraulics.

Control accuracy is one of the benefits of the hydraulic system over others. Careless usage and lack of maintenance will create hydraulic problems.

### 11.6: Gauge Pressure, Absolute Pressure, and Pressure Measurement

Most of the problems in the hydraulic system can be eliminated with proper care and maintenance. There are some common hydraulic problems that can be detected easily.

The important symptoms of system failures include abnormal noise, high fluid temperature and slow operation. The ultimate aim of this article is to help you to detect the problems and hydraulic solutions to resolve them. Hydraulic troubleshooting is not an easy task. You can find the solution for all hydraulic system problems through step by step procedures.

Some common hydraulic trouble causes and hydraulic solutions are listed below. Hydraulic system performance related issues can be categorized into inoperative, slow operation, fast operation and unpredictable operations. The root cause for all these will be different we can discuss some common causes and their solutions. Overheating of oil can be an indication of serious failures.

Not only failures, but this is also a safety concern for the industry. Foaming of oil is another problem related to hydraulic fluids. Aeration and cavitation are the common hydraulic pump problems.

We can discuss other issues and their resolving techniques here. A hydraulic cylinder is a mechanical actuator for generating unidirectional force. The common hydraulic problems of hydraulic cylinder are. Hydraulic System Problems and Solutions Hydraulic systems are part of the fluid power industry. Problems related to Hydraulic system performance Hydraulic system performance related issues can be categorized into inoperative, slow operation, fast operation and unpredictable operations.

Fill the system with suitable oil as per the specification. Also, check for leakage. Dirty or clogged filter: Filters plays a vital role in removing the contaminants present in the oil. This can be a reason for an inoperative system, slow operation, and unpredictable operation. To resolve this issue you want to drain the oil and replace filter or filter element. Other worn or dirty components will also cause these issues.

Excess load: Excess load in the system will stop the operation or slow down the operation.Matter most commonly exists as a solid, liquid, or gas; these states are known as the three common phases of matter. We will look at each of these phases in detail in this section. Solids are rigid and have specific shapes and definite volumes. The atoms or molecules in a solid are in close proximity to each other, and there is a significant force between these molecules.

Solids will take a form determined by the nature of these forces between the molecules. Although true solids are not incompressible, it nevertheless requires a large force to change the shape of a solid. In some cases, the force between molecules can cause the molecules to organize into a lattice as shown in Figure.

## 11.6: Gauge Pressure, Absolute Pressure, and Pressure Measurement

The structure of this three-dimensional lattice is represented as molecules connected by rigid bonds modeled as stiff springswhich allow limited freedom for movement. Even a large force produces only small displacements in the atoms or molecules of the lattice, and the solid maintains its shape. Solids also resist shearing forces. Shearing forces are forces applied tangentially to a surface, as described in Static Equilibrium and Elasticity. Liquids and gases are considered to be fluids because they yield to shearing forces, whereas solids resist them.

Like solids, the molecules in a liquid are bonded to neighboring molecules, but possess many fewer of these bonds. The molecules in a liquid are not locked in place and can move with respect to each other. The distance between molecules is similar to the distances in a solid, and so liquids have definite volumes, but the shape of a liquid changes, depending on the shape of its container. Gases are not bonded to neighboring atoms and can have large separations between molecules.

Gases have neither specific shapes nor definite volumes, since their molecules move to fill the container in which they are held Figure. Figure Forces between the atoms strongly resist attempts to compress the atoms. A gas must be held in a closed container to prevent it from expanding freely and escaping. Liquids deform easily when stressed and do not spring back to their original shape once a force is removed. This occurs because the atoms or molecules in a liquid are free to slide about and change neighbors. That is, liquids flow so they are a type of fluidwith the molecules held together by mutual attraction. When a liquid is placed in a container with no lid, it remains in the container. Because the atoms are closely packed, liquids, like solids, resist compression; an extremely large force is necessary to change the volume of a liquid.

In contrast, atoms in gases are separated by large distances, and the forces between atoms in a gas are therefore very weak, except when the atoms collide with one another. This makes gases relatively easy to compress and allows them to flow which makes them fluids. When placed in an open container, gases, unlike liquids, will escape. In this chapter, we generally refer to both gases and liquids simply as fluids, making a distinction between them only when they behave differently.