Bernoulli pressure

The Reynolds number in this example is approximately 2 and this may go some way towards explaining the discrepancy between the two pressures. The two calculated pressures apply to low and high Reynolds nunber flows respectively so that the real pressure probably lies between the two calculated pressures. However the results show that a disparity may arise when using the Bernoulli pressure head to find a maximum pressure in a given problem. 

Pitot Tubes. The fundamental design of a pitot tube is shown in Eigure 9a. The opening into the flow stream measures the total or stagnation pressure of the stream whereas a wall tap senses static pressure. The velocity at the tip opening, lA can be obtained by the Bernoulli equation ... 

Head-Area Meters. The Bernoulli principle, the basis of closed-pipe differential-pressure flow measurement, can also be appHed to open-channel Hquid flows. When an obstmction is placed in an open channel, the flowing Hquid backs up and, by means of the Bernoulli equation, the flow rate can be shown to be proportional to the head, the exact relationship being a function of the obstmction shape. 

Two types of floater aozzles are curreafly ia use and they are based on two different principles. The Bernoulli principle is used ia the airfoil flotatioa aozzles, ia which the air flows from the aozzle parallel to the web and the high velocities create a reduced pressure, which attracts the web while keeping the web from touching the nozzles. The Coanda effect is used to create a flotation nozzle when the air is focused and thus a pressure pad is created to support the web as shown ia Figure 19. 

The impeller is attached to a shaft. The shaft spins and is powered by the motor or driver. We use the term driver because. some pumps are attached to pulleys or transmissions. The fluid enters into the eye of the impeller and is trapped between the impeller blades. The impeller blades contain the liquid and impart speed to the liquid as it passes from the impeller eye toward the outside diameter of the impeller. As the fluid accelerates in velocity, a zone of low pressure is created in the eye of the impeller (the Bernoulli Principle, as velocity goes up, pressure goes down). This is another reason the liquid must enter into the pump with sufficient cnergt. ... 

According to Bernoulli s Law, when velocity goes up, pressure goes down. This was explained in Chapter 1. A centrifugal pump works by acceleration and imparting velocity to the liquid in the eye of the impeller. Under the right conditions, the liquid can boil or vaporize in the eye of the impeller. When this happens we say that the pump is suffering from vaporization cavitation. 

The other ease is when there is too niiieh flow through the pump. The pump is operating to the right of the BEP on its eurve (Figure 9-8). The same problem oceurs, but now in the other direction. With the severe increase in velocity through the pump, the pressures tall dramatically in the H-F-G-H arc of the volute circle (Bernoulli s Law-says that as velocity goes up, pressure comes down). Now the shaft deflects, or even breaks in the opposite direction. .. at approximately 240° around the volute from the cutwater. 

Bernoulli effect At any point in a conduit through which a liquid is flowing, the sum of pressure energy, potential energy, and kinetic energy is constant. 

Volume 1 explains that pumps ean be classified as either positive-displacement or kinetie. The same is true for compressors. In a positive displacement compressor the gas is transported from low pressure to high pressure in a device that reduces its volume and thus inereases its pressure. The most common type of positive displacement eompressors are reeiprocating and rotary (serew or vane) just as was the ease for pumps. Kinetic compressors impart a veloeity head to the gas, which is then converted to a pressure head in accordance with Bernoulli s Law as the gas is slowed down to the velocity in the discharge line. Just as was the case with pumps, centrifugal compressors are the only form of kinetic compressor commonly used. 

The result that Archimedes discovered was the first law of hydrostatics, better known as Archimedes Principle. Aixhimedes studied fluids at rest, hydrostatics, and it was nearly 2,000 years before Daniel Bernoulli took the next step when he combined Archimedes idea of pressure with Newton s laws of motion to develop the subject of fluid dynamics. 

Bernoulli and Euler dominated the mechanics of flexible and elastic bodies for many years. They also investigated the flow of fluids. In particular, they wanted to know about the relationship between the speed at which blood flows and its pressure. Bernoulli experimented by puncturing the wall of a pipe with a small, open-ended straw, and noted that as the fluid passed through the tube the height to which the fluid rose up the straw was related to fluid s pressure. Soon physicians all over Europe were measuring patients blood pressure by sticking pointed-ended glass tubes directly into their arteries. (It was not until 1896 that an Italian doctor discovered a less painful method that is still in widespread... 

Hydrodynamic marked the beginning of fluid dynamics—the study of the way fluids and gases behave. Each particle in a gas obeys Isaac Newton s laws of motion, but instead of simple planetary motion, a much richer variety of behavior can be observed. In the third century B.C.E., Archimedes of Syracuse studied fluids at rest, hydrostatics, but it was nearly 2,000 years before Daniel Bernoulli took the next step. Using calculus, he combined Archimedes idea of pressure with Newton s laws of motion. Fluid dynamics is a vast area of study that can be used to describe many phenomena, from the study of simple fluids such as water, to the behavior of the plasma in the interior of stars, and even interstellar gases. 

Bernoulli s equation (Equation 2-53), which accounis for static and dynamic pressure losses (due to changes in velocity), but does not account for frictional pressure losses, energ losses due to heat transfer, or work done in an engine. 

Flow through chokes and nozzles is a special case of fluid dynamics. For incompressible fluids the problem can be handled by mass conservation and Bernoulli s equation. Bernoulli s equation is solved for the pressure drop across the choke, assuming that the velocity of approach and the vertical displacement are negligible. The velocity term is replaced by the volumetric flow rate times the area at the choke throat to yield... 

The theory of pressure losses can be established by developing Bernoulli s theorem for the case of a pipe in which the work done in overcoming frictional losses is derived from the pressure available. For a fluid flowing in a pipe, the pressure loss will depend on various parameters. If... 

At all points in a system, the static pressure is always equal to the original static pressure less any velocity head at a specific point in the system and less the friction head required to reach that point. Since both the velocity head and friction head represent energy and energy cannot be destroyed, the sum of the static head, the velocity head, and the friction head at any point in the system must add up to the original static head. This is known as Bernoulli s principal, which states For the horizontal flow of fluids through a tube, the sum of the pressure and the kinetic energy per unit volume of the fluid is constant. This principle governs the relationship of the static and dynamic factors in hydraulic systems. 

Equation 2.43 is known as Bernoulli s equation, which relates the pressure at a point in the fluid to its position and velocity. Each term in equation 2.43 represents energy per unit mass of fluid. Thus, if all the fluid is moving with a velocity u, the total energy per unit mass ijf is given by ... 

That the stream velocity does not change in the direction of flow. On this basis, from Bernoulli s theorem, the pressure then does not change (that is, dP/dx — 0). In practice, 3P/ dx may be positive or negative. If positive, a greater retardation of the fluid will result, and the boundary layer will thicken more rapidly. If dP/ dx is negative, the converse will be true. 

The force produced as a result of any difference in pressure dP between the planes 3-4 and 1-2. However, if the velocity us outside the boundary layer remains constant, from Bernoulli s theorem, there can be no pressure gradient in the X-direction and dP/dx = 0. 

The instantaneous velocity is then used to estimate the instantaneous local static pressure using Bernoulli s equation of the following form ... 

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