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a = angle of attack; t = transverse moment of inertia; d = air density; v = velocity; Thus, Miller essentially took Greenhill's rule of thumb and expanded it slightly, while keeping the formula simple enough to be used by someone with basic math skills. To improve on Greenhill, Miller used mostly empirical data and basic geometry.
where is the applied tension on the line, is the resulting force exerted at the other side of the capstan, is the coefficient of friction between the rope and capstan materials, and is the total angle swept by all turns of the rope, measured in radians (i.e., with one full turn the angle =).
Static measurements yield values in-between the advancing and receding contact angle depending on deposition parameters (e.g. velocity, angle, and drop size) and drop history (e.g. evaporation from time of deposition). Contact angle hysteresis is defined as θ A – θ R although the term is also used to describe the expression cos θ R – cos ...
The Reynolds number Re is taken to be Re = V D / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where ν is the kinematic viscosity μ / ρ, with μ the fluid's Dynamic viscosity, and ρ the fluid's density. The pipe's relative roughness ε / D, where ε is the pipe's effective roughness height and D the pipe ...
is the angle of the tube with respect to the horizontal axis. ϕ {\displaystyle \phi } is the contact angle of the liquid on the capillary material. Substituting these expressions leads to the first-order differential equation for the distance the fluid penetrates into the tube l {\displaystyle l} :
Tension is the pulling or stretching force transmitted axially along an object such as a string, rope, chain, rod, truss member, or other object, so as to stretch or pull apart the object. In terms of force, it is the opposite of compression. Tension might also be described as the action-reaction pair of forces acting at each end of an object.
They gave those formulas in two forms: in the basic and using standardized variables. If one assumes that N asperities covers a rough surface, then the expected number of contacts is = The expected total area of contact can be calculated from the formula
velocity in terms of the speed of light c: unitless beta particle: gamma: Lorentz factor: unitless photon: gamma ray: shear strain: radian heat capacity ratio: unitless surface tension: newton per meter (N/m) delta: change in a variable (e.g. ) unitless Laplace operator: per square meter (m −2)