Question

The goal of a diffuser is to slow down flow from high velocities to low velocities. In this diffuser, air is flowing at 3.8 kg/s and enters the diffuser at 265 m/s and 302 K. What is the velocity of the flow at the outlet (in m/s) if the final temperature is 307 K? Use cp-1001 J/kg-K for air. If changes in kinetic and potential energy are negligible, the passive heating of a fluid means which of the following in a steady-flow control volume: a Δh > 0 b Δh < 0 c ΔT > 0 d ΔT < 0

Answer 1

To solve for the outlet velocity, we need to use the conservation of mass and conservation of energy equations:

Conservation of mass: m1 = m2

where m1 is the mass flow rate at the inlet and m2 is the mass flow rate at the outlet

Conservation of energy: (m1 * u1 * cp) + (m1 * h1) = (m2 * u2 * cp) + (m2 * h2)

where u1 and u2 are the velocities at the inlet and outlet. h1 and h2 are the enthalpy values at the inlet and outlet.

Therefore, we can solve for u2, the velocity at the outlet:

u2 = ((m1*u1*cp) + (m1*h1) - (m2*h2)) / (m2*cp)

Plugging in the given values:

u2 = ((3.8 kg/s*265 m/s*1001 J/kg-K) + (3.8 kg/s*1520.4 kJ/kg) - (3.8 kg/s*1537.1 kJ/kg)) / (3.8 kg/s*1001 J/kg-K)

u2 = 253.4 m/s

For the second part of your question, the passive heating of a fluid in a steady-flow control volume means that Δh > 0. Since the flow is steady, there is no change in kinetic or potential energy, and therefore the total enthalpy change must be greater than zero.