Fluid power formulas

A formula is used in computing force, pressure, and area in fluid power systems. In this formula, P refers to pressure F indicates force, and A represents area. Force equals pressure times area. Thus, the formula is written ... 

By using mathematical formiflas, engineers can design, calculate, and control fluid power systems. Many of these formulas were developed centuries ago. 

For a Power law fluid flow, the following formulas can be used Pipe flow... 

We now have a very nice formula for the outlet temperature and the heating power. The heating power is the maximum power possible if the full temperature rise can be reached multiplied by a factor that incorporates the ratio of the heat exchanger quality to the fluid parameters. 

The simple formula derived for viscosity in Eq. 12.49 predicts that /z should be independent of pressure and should increase as the square root of temperature. It is typically found that the viscosity of a gas is independent of pressure except at high and low pressure extremes. At very high pressure, molecular interactions become more important and the rigid-sphere approximation becomes inappropriate, leading to a breakdown in Eq. 12.49. At very low pressures, the gas no longer behaves like a continuum fluid, and the steady-state flow picture of Fig. 12.1 is no longer valid. Viscosity is usually found experimentally to increase with T faster than the n = 1 /2 power. Consideration of the interaction potential between molecules, as is discussed in the next section, is needed to more closely match the observed temperature dependence of /x. 

Given the success of the encounter theory in modeling D/Dg for selfdiffusion in dense fluids, in Section III B, the question arises as to whether its extension into the frequency regime is possible. The formula for in Eq. (3.8) was derived by linear response as an extension of the zero-frequency result. There are two terms that need to be evaluated—the force power sjjectrum < / (oj) > and the flux Jt( w)-... 

The plates are a distance of 0.005 m apart, and the applied pressure gradient is 60 Pa in a length of 0.3 m. The density of the fluid is that of water. (Hint Follow the steps in the example of entry flow in a pipe, except use a power-law formula for viscosity and use two flat plates rather than a pipe.)... 

Problem (6.6.7) up to notation coincides with the classical thermal explosion problem [133], This fact together with formula (6.6.6) allows one to find the temperature distribution in the tube for a nonisothermal flow of a power-law fluid [50], Namely,... 

The main dimensionless parameter for power-law fluids is the generalized Reynolds number introduced by the formula... 

In the case of an inertia-free flow (at low Reynolds numbers) of a quasi-Newtonian power-law fluid with rheological index n close to 1 past a gas bubble, the drag coefficient can be calculated by the formula [190]... 

The velocity of a drop falling by gravity in a power-law fluid at low Reynolds numbers is given by the formula [69]... 

In the case of mass exchange between a bubble and a translational Stokes flow of a quasi-Newtonian power-law fluid (n is close to unity), one can use the following simple approximate formula for calculating the mean Sherwood number at high Peclet numbers ... 

For fluids following the power-law model the velocity variation with radius follows the formula... 

A great deal of work was done by Orzechowski [69] for twin fluid rotary atomizers under very well defined conditions (see Table 24.11). He proposed two correlations one for when the atomizing surface was a disk with no rims 24.1 l.vi, and one for when the atomizing surface was a cup with rims 24.1 l.vii. In the latter case, the rim properties are also taken into account. One key difference between the two formulas is that for rotating disks, liquid film thickness is said to have an effect and SMD proportional to In the case of rotating cups, liquid film thickness is said to have no effect on the atomization, and instead the volumetric flow rate of the liquid does. Also, U is raised to the power of 2 instead of —3. 

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