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
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