Why velocity gradient is necessary for viscous force?

To keep one layer of fluid moving at a greater velocity than the adjacent layer, a force F is necessary, resulting in a shearing stress F/A, where A is the area of the surface in contact with the layer being moved. …

What are the conditions for flow to be irrotational?

Irrotational flow is a flow in which each element of the moving fluid undergoes no net rotation with respect to a chosen coordinate axes from one instant to other. A well-known example of irrotational motion is that of the carriages of the Ferris wheel (giant wheel).

What is the direction of velocity gradient?

and the direction of the velocity gradient is perpendicular to the direction of the tangential force on the liquid due to other layers.

What causes the no slip condition?

In fluid dynamics, the no-slip condition for viscous fluids assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary. The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary.

How velocity gradient is related to viscosity?

The viscosity is defined as the shear force per unit area necessary to achieve a velocity gradient of unity. Equation 5.2 applies to the majority of fluids, and they are generally known as Newtonian fluids, or fluids that display Newtonian behaviour.

What is the relation between viscous force and the velocity gradient?

The viscous drag is directly proportional to the velocity gradient. The coefficient of viscosity depends on the nature of the liquid. Hence, the viscous drag is dependent on the nature of the liquid. The viscous force acts parallel to layers.

What is velocity potential in irrotational flow?

12.2 Velocity Potential This function ϕ is called velocity potential, and such a flow is called potential or irrotational flow. In other words, the velocity potential is a function whose gradient is equal to the velocity vector.

How do you know if a flow is irrotational or rotational?

To classify any flow as Rotational or Irrotational the angular motion of the fluid elements is analyzed. If the angle between the two intersecting lines of the boundary of the fluid element changes while moving in the flow, then the flow is a Rotational Flow.

What is velocity gradient in steady flow?

Velocity gradient in steady flow is defined as the rate at which velocity changes as a function of distance from the stationary layer. When the magnitude of velocity varies distance it is referred to as Velocity gradient. Here distance refers to the distance between the adjacent layers of fluid.

How do you find the gradient of a velocity?

Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates for these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

What is slip velocity?

Slip velocity is the difference between the velocity of the conveying air and that of the conveyed particles. Slip ratio is the dimensionless ratio of the velocity of a particle, Cp, divided by the velocity of the conveying air, Ca.

What is slip flow?

n. (General Physics) physics gas flow occurring at hypersonic speeds in which molecular shearing occurs.