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Phase and group velocity divided by √ gh as a function of h / λ . A: phase velocity, B: group velocity, C: phase and group velocity √ gh valid in shallow water. Drawn lines: based on dispersion relation valid in arbitrary depth. Dashed lines: based on dispersion relation valid in deep water.
If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. A ...
The linear velocity of a rigid body is a vector quantity, equal to the time rate of change of its linear position. Thus, it is the velocity of a reference point fixed to the body. During purely translational motion (motion with no rotation), all points on a rigid body move with the same velocity.
Settling velocity W s of a sand grain (diameter d, density 2650 kg/m 3) in water at 20 °C, computed with the formula of Soulsby (1997). When the buoyancy effects are taken into account, an object falling through a fluid under its own weight can reach a terminal velocity (settling velocity) if the net force acting on the object becomes zero.
which is a Bernoulli equation valid also for unsteady—or time dependent—flows. Here ∂φ / ∂t denotes the partial derivative of the velocity potential φ with respect to time t, and v = | ∇φ | is the flow speed. The function f(t) depends only on time and not on position in the fluid.
It consists of a pot with a small hole at the bottom through which the water can escape. The amount of escaping water gives the measure of time. As given by the Torricelli's law, the rate of efflux through the hole depends on the height of the water; and as the water level diminishes, the discharge is not uniform.
Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by shallow-water phase velocity √ gh as a function of relative depth h / λ. Blue lines (A): phase velocity; Red lines (B): group velocity; Black dashed line (C): phase and group velocity √ gh valid in shallow water.
Slender-body theory is a methodology used in Stokes flow problems to estimate the force on, or flow field around, a long slender object in a viscous fluid. The shallow-water equations can be used to describe a layer of relatively inviscid fluid with a free surface, in which surface gradients are small.