Floating in the Swiftness of Time

Rapidly varying flow (RVF) in open channels is characterized by abrupt changes in flow depth over a short distance, with the rate of depth change relative to distance often approaching unity. These flows are inherently complex due to their transient and multi-dimensional nature, making exact analysis difficult. However, approximate solutions using simplified models provide valuable insights into their behavior.Key Features of Rapidly Varying FlowRVF is commonly observed in scenarios involving...

When an object is placed in a fluid, it either floats or sinks. All objects in a fluid experience a buoyant force. For example, a metal ball sinks, while a rubber ball floats. Similarly, a submarine can sink and float by adjusting its buoyancy.  The concept of buoyancy raises several interesting questions. For instance, where does this buoyant force come from? How much buoyant force is required to make an object sink or float? Do objects that sink get any support at all from the...

When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:

Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of displacement with respect to time. Like average velocity, the instantaneous velocity is a vector with the dimensions of length per unit time. Instantaneous velocity can have both positive and negative values. The instantaneous velocity can be...

An object falling without any air resistance under the influence of gravitational force is said to be in free-fall. For free-falling bodies, the acceleration due to gravity is constant, irrespective of their mass. Free-fall is experienced not only by objects falling downward, but also by all objects whose motion is influenced by gravitational force alone. The dynamics of free-fall motion can be calculated using kinematic equations of motion, since free-fall acceleration is constant.
The...

The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To calculate this, it is important to know the instantaneous velocity, which is the velocity at a specific instant of time or at a specific point along the path. Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity vx of an object is the limit of the average...