determine the magnitue and direction of the anchoring force

The ambient pressure is usually atmospheric. An incompressible jet has an exit pressure equal to.Here are some rules when using the momentum equation. The final form of the momentum equation for steady flow with one.Types of forces include struts, bolts, cables, ropes in tension, forces On the control volume that is not accounted for. Finally let us consider other surface forces.

The viscous term as are unknown term and solve for it by computing our Of the control surface has viscous forces acting on it. This is done by picking a control volume so that no part We can often choose a 'wise' control volume to eliminate thisĭifficult term. Fortunately we usually do not have to integrate for this term. Term you would have to integrate the shear stress over the entire control This force is difficult to calculate because it has a normal and a tangentialĬomponent acting in an arbitrary direction.

Now let us return to the viscous forces.

Pressure field has zero net pressure force. This holds true because any shape in a uniform We realize that the sum of the forcesĭue to pressure is the same in both cases. Realizing theĭefinition of gage pressure, Pg = Pabsolute - Patmospheric, we can subtractĪtmospheric pressure from everything. Suppose there is a high pressureĪt two locations and atmospheric pressure everywhere else. Long as you are consistent everywhere! To prove this, consider an arbitraryĬontrol volume with a certain pressure field. You can use either absolute or gage pressure in this equation as P is always defined as positive inward and n is always definedĪs positive outward.

Other-forces due to control volume cutting through bolts.

Viscous-viscous and frictional forces contribute normal.

Pressure-contributes only normal forces.

Gravity is a body force that acts in the negative z-direction. There are several types of forces that can act on This term represents the sum of all the forces acting

Now lets return to the left side of the CLM equation.

Since the velocity vector = (u,v,w) and the force vector = (F x,F y,F z), ourĮquation can be rewritten into three equations: Inlets and outlets with constant density. Most of the problems we deal with having steady flow also have one dimensional

If the flow is steady we can drop the (d/dt) term.

We can make a further simplification if we notice that the definitionįor mass flow rate is (density)(velocity)(area). This holds true because V dot n = V for outlets and -V for We can rewrite the last term in our CLM equation: Is constant across the inlet or outlet surface. This implies that our velocity vector V is parallel

First, let us assume that we have one dimensional inletsĪnd outlets.

It is now time for a few simplifications for the right.

Similarly, the conservation of momentum could be applied.The conservation of linear momentum applied to the y-direction becomes: Next, let us consider the component in the Y-direction.Notice that the V dot n term is a scalar, not

We will drop the cv subscript since it is understood.

First, let us consider the component in the X-direction.

This is a vector equation so it has three components.

For a fixed control volume we have the following.

So, the forces of the system are the same at theįorces of the control volume at a given instant. NOTE: Recall that at any instant of time t, the system Use in a control volume, use RTT with B = m V, beta Recall the conservation of linear momentum law for Conservation of Momentum using Control Volumes Conservation of Momentum using Control Volumes Conservation of Linear Momentum

Determine the magnitue and direction of the anchoring force