Bernoulli for incompressible inviscid flow

[Emzielou83]

1. Investigate and apply equations of stae; speed of sound; continuity; bernoulli for incompressible inviscid flow; shear forces and stresses; laminar flow; flow in boundary layer link to shear forces and viscosity- continuity equation


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3. I have answered 90% of the question. What I don't get is the last bit - flow in boundary layer link to shear forces and viscosity- continuity equation.

I understand continuity is Mass can neither be created nor destroyed. and the formula for steady flow is ρ1A1V1= ρ2A2V2 . I understand boundary layer is the point at which no dragging effect occurs.

I also understand that viscosity effects the flow over the wing of an aircraft but surely this is the same as laminar and turbulant flow??

I don't understand the link between viscosity and continuity.

Can anyone help please??

 

[KataKoniK]

it is important to understand the connections between different concepts and equations in order to fully comprehend a system or phenomenon. In this case, the link between viscosity and continuity can be explained through the concept of shear forces.

Viscosity is a measure of a fluid's resistance to flow. In other words, it is a measure of how "thick" or "sticky" a fluid is. When a fluid flows, it experiences shear forces, which are forces that act parallel to its surface. These shear forces are responsible for the friction and drag experienced by objects moving through the fluid. In the case of a boundary layer, the shear forces are particularly important as they determine the flow behavior near the surface of an object, such as an aircraft wing.

Now, let's consider the continuity equation. This equation states that the mass flow rate in a system must remain constant. In other words, the amount of fluid entering a certain area must be equal to the amount of fluid leaving that area. This is where the link to viscosity comes in.

In a boundary layer, the fluid near the surface experiences a higher shear force due to its proximity to the surface. This shear force causes the fluid to slow down, and as a result, the velocity of the fluid near the surface is lower than the velocity of the fluid further away from the surface. This difference in velocity creates a gradient in the fluid's velocity, known as the velocity gradient. This gradient is directly related to the shear stress experienced by the fluid, which is a measure of the force per unit area acting on the fluid.

Now, let's consider the continuity equation again. If we have a fluid with a non-uniform velocity profile, the mass flow rate must still remain constant. This means that the fluid near the surface, with a lower velocity, must have a higher density to compensate for the lower velocity. This is where the viscosity comes in. Viscosity is a measure of a fluid's internal resistance to flow, and a higher viscosity means that the fluid has a higher internal friction. This higher internal friction results in a higher density near the surface, which balances out the lower velocity and ensures that the mass flow rate remains constant.

In summary, the link between viscosity and continuity can be explained through the concept of shear forces. The shear forces experienced by a fluid in a boundary layer are directly related to the velocity gradient, which in turn affects the density of the fluid. This connection between velocity, shear