A well-insulated tank in a vapor power plant operates at steady state. Saturated liquid water enters at inlet 1 at a rate of 125
lbm/s at 14.7 psia. Make-up water to replenish steam losses from the plant enters at inlet 2 at a rate of 10 lbm/s at 14.7 psia and 60o F. Water exits the tank at 14.7 psia. Neglect kinetic and potential energy effects, determine for the water exiting the the tank (a) the mass flow rate, in lb/s. (b) the specific enthalpy, in Btu/lb (c) the temperature, in F
<h2> We now focus on purely two-dimensional flows, in which the velocity takes the form
</h2><h2>u(x, y, t) = u(x, y, t)i + v(x, y, t)j. (2.1)
</h2><h2>With the velocity given by (2.1), the vorticity takes the form
</h2><h2>ω = ∇ × u =
</h2><h2></h2><h2>∂v
</h2><h2>∂x −
</h2><h2>∂u
</h2><h2>∂y
</h2><h2>k. (2.2)
</h2><h2>We assume throughout that the flow is irrotational, i.e. that ∇ × u ≡ 0 and hence
</h2><h2>∂v
</h2><h2>∂x −
</h2><h2>∂u
</h2><h2>∂y = 0. (2.3)
</h2><h2>We have already shown in Section 1 that this condition implies the existence of a velocity
</h2><h2>potential φ such that u ≡ ∇φ, that is
</h2><h2>u =
</h2><h2>∂φ
</h2><h2>∂x, v =
</h2><h2>∂φ
</h2><h2>∂y . (2.4)
</h2><h2>We also recall the definition of φ as
</h2><h2>φ(x, y, t) = φ0(t) + Z x
</h2><h2>0
</h2><h2>u · dx = φ0(t) + Z x
</h2><h2>0
</h2><h2>(u dx + v dy), (2.5)
</h2><h2>where the scalar function φ0(t) is arbitrary, and the value of φ(x, y, t) is independent
</h2><h2>of the integration path chosen to join the origin 0 to the point x = (x, y). This fact is
</h2><h2>even easier to establish when we restrict our attention to two dimensions. If we consider
</h2><h2>two alternative paths, whose union forms a simple closed contour C in the (x, y)-plane,
</h2><h2>Green’s Theorem implies that
</h2><h2></h2><h2></h2><h2></h2><h2></h2><h2></h2><h2></h2><h2></h2>
