Bernoulli s theorem

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... 

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. 

This is a statement of Bernoulli s theorem the quantity v2l2+Plp+gh is constant throughout the fluid for steady, irrotational flow. Equation A.33 is the same as equation 1.11. It will be recalled that, for rotational flow with friction, the engineering form of Bernoulli s equation applies only along a streamline and allowance must be made for frictional losses. 

At the nose, viscous forces can be neglected, and therefore the velocity in the liquid film can be calculated from Bernoulli s theorem. Nicklin et al. show that for these assumptions... 

This conception is useful in aerodynamics as the dynamic pressure represents the unit air pressure acting on a surface increment in almospheric air moving with velocity V over the surface. By Bernoulli s theorem. 

Equation (5.52) is Bernoulli s theorem [16], an energy equation that is well known to be equal to the sum of the elevation head, the pressure head, and the velocity head. Here the elevation head has been left out because the fan suction air pressure and the exiting air pressure from the air cooler are both equal. 

The equation in either of these last two forms is known as Bernoulli s theorem, in honor of Daniel Bernoulli, who presented it in 1738. Note that Bernoulli s theorem is for a frictionless, incompressible fluid only. 

Jet trajectory. A free liquid jet in air will describe a trajectory, or path under the action of gravity, with a vertical velocity component which is continually changing. The trajectory is a streamline consequently, if air friction is neglected, Bernoulli s theorem may be applied to it, with all the pressure terms 0. Thus, the sum of the elevation and velocity head must be the same for all points of the curve. The energy gradient is a horizontal line at distance V2/2g above the nozzle, where V is the velocity leaving the nozzle. 

Head-type flow measurement derives from Bernoulli s theorem. Work on the conventional orifice plate for gas flow measurement was commenced by Weymouth in the United States in 1903. 

Venturi tubes, flow nozzles, and flow tubes, similar to all differential pressure producers, are based on Bernoulli s theorem. Meter coefficients for venturi tubes and flow nozzles are approximately 0.98-0.99, whereas for orifice plates it averages about 0.62. Therefore, almost 60% (98/62) more flow can be obtained through these elements for the same differential pressure (see Figure 3.82). 

Compute the pressure at section 2. Use Bernoulli s theorem, which in one form can be written... 

In chapter 2 the framework of this study will be defined and advantage will be taken of Bernoulli s theorem to define and understand clearly the interest of flow curves. They constitute an important tool and are characteristic of the instabilities likely to occur. 

Streamlines are hypothetical lines without width drawn parallel to all points to the motion of the fluid. As velocity increases, pressure decreases. Pressure field around an object is the reverse of velocity field. This may appear to contradict common experience. However, it follows from the principle of conservation of energy and finds expression in Bernoulli s theorem. 

Figure 2.12 Illustration of Bernoulli s theorem. The fluid (or gas) flows more rapidly at B than A or C, and the pressure is less at B than A or C.

The kinetic-energy correction factor may be important in applying Bernoulli s theorem between stations when one is in laminar flow and the other in turbulent flow. Also, factors a and p are of some importance in certain types of compact heat-exchange equipment, where there are many changes in size of the fluid channel and where the tubes or heat-transfer surfaces themselves are short. In most practical situations both are taken as unity in turbulent flow. 

BERNOULLI S THEOREM - In stream of liquid, the sum of elevation head, pressure head and velocity remains constant along any line of flow provided no work is done by or upon liquid in course of its flow, and decreases in proportion to energy lost in flow. 

At this stage, the basic principle of gas induction (Bernoulli s theorem) was invoked. White and de Villiers used dimensional considerations to define the critical suction due to impeller rotation by... 

Bernoulli s theorem bor- nii-lez- [Daniel Bernoulli t 1 82 Swiss physicist]. At any point in a tube through which a liquid is flowing the sum of the pressure energy, potential energy, and kinetic energy is constant. If p is pressure /z, height above the reference plane d, density of the liquid, and V, velocity of flow,... 

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