Question

The nozzle throat area is same as the diffuser throat area.

(a) True

(b) False

I have been asked this question in homework.

This intriguing question originated from Supersonic Wind Tunnels topic in division Compressible Flow through Nozzles, Diffusers and Wind Tunnels of Aerodynamics

Answer 1

Correct choice is (b) False

Explanation: If we consider the nozzle throat area as section 1, then the mass flow rate through the section is \(\dot {m_1}\) = ρ1u1A1t. The mass flow rate through th diffuser throat area is \(\dot {m_2}\) = ρ2u2A2t. Since there’s steady flow in side the wind tunnel, thus the mass flow rate remains same.

\(\dot {m_1} = \dot {m_2}\)

ρ1u1A1t = ρ2 u2A1t

But due to the presence of shock waves inside the diffuser, the density and the flow velocity are not same. (ρ1≠ρ2, u1≠u2). This means that the throat areas are also not same.