Terminal velocity is the maximum velocity that a falling object can reach when the drag force of the surrounding fluid is equal to the object's weight. At this point, the object will no longer accelerate and will continue to fall at a constant speed.
The formula for calculating terminal velocity in turbulent flow for a spherical object is: Vt = √(2mg/ρACd), where Vt is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the object, and Cd is the drag coefficient.
Turbulent flow is a type of fluid flow in which the fluid particles move in a chaotic and irregular manner. This type of flow is characterized by high velocities, eddies, and vortices, and is commonly observed in situations where there are high velocities or large changes in direction.
The shape of an object can greatly affect its terminal velocity in turbulent flow. Objects with a larger cross-sectional area or a more streamlined shape will experience more drag and have a lower terminal velocity, while objects with a smaller cross-sectional area or a less streamlined shape will experience less drag and have a higher terminal velocity.
Besides the mass, shape, and density of the object and the density of the fluid, other factors that can affect terminal velocity in turbulent flow include the viscosity of the fluid, the roughness of the object's surface, and the presence of other objects or obstacles in the flow. These factors can all impact the magnitude and direction of the drag force acting on the object, thus affecting its terminal velocity.