The Euler equations with frictional force have been extensively studied. Since the Boltzmann equation is closely related to the equations of gas dynamics, we study, in this paper, the Boltzmann equation with frictional force when the external force is proportional to the macroscopic vel...
aIn this equation for force balance on the control volume the acceleration term is equal to the static pressure and frictional forces acting on the control volume. 在这个等式为力量平衡在控制体积加速度期限与行动在控制体积的静压和摩擦力是相等的。 [translate] ...
The magnitude of the frictional force is often directly proportional to the normal force, or the force pressing the two surfaces against each other. The constant of proportionality varies depending on the surfaces which are in contact. For example, you might expect smaller friction when two "slick...
Just like flow through a pipe, the frictional force relies on the flow’s laminarity and certain gas characteristics. To account for a wider range of flow regime, the Ergun equations is used as it can handle both laminar and turbulent flows. The Ergun equation is shown in Eq. (5). (5...
There is a downward gravitational force equal to mg , where g is the acceleration due to gravity. There is also a frictional force resisting the motion, which we assume to be proportional to the speed of the bob with a coefficient of friction k . Using Newton's second law of motion, ...
In the case of spherical particles, the translational frictional force f is proportional to the fluid viscosity,η, and radius r of the particle. Thus the coefficient of friction for spherical par- ticles, known as Stokes law, is f = 6phr. (3) The frictional coefficient f comes into ...
it. That would work fine if you assume the direction of v (and hence the force) is vertical. In the more general case where you don't assume the direction of v is vertical, then -kv|v| would describe both the direction of the frictional force (since v is a vector) and the ...
There are three force relevant to the mass: frictional force, gravitational force, and string tension (on the left and right of the mass). For string tension, you may make approximation: [tex] sin\theta \approx tan\theta \approx \frac{dy}{dx}[/tex] Solve these these equation with ...
2.1.3 Const i t ut i ve l aws: Appl i ed for ces In this section, we describe the external forces on the pendulum. We will assume three types of forces: 1. The force of gravity f g , 2. Viscous or frictional forces f v , 3. The force of constraint applied by the pivot f...
where b¯u1 is the equivalent frictional force of motor/arm, I0 is the transverse moment of inertia for arm at the fixed point B, τ is the torque applied to the arm by the motor. Substituting for T1,T2andFϕ1 at their directions defined in Eqs. (14), (15) and (12) respectiv...