How many board feet in a piece of Oak that is 1" thick, 6 inches wide and 8' long?

a. 4.279 MPa

b. 3.198 MPa to 4.279 MPa

c. 0.939 MPa

d. Below 3.198 MPa

Explanation:

From the given parameters

M = 1.75 MPa  

M at 1.6 MPa gives A/A* = 1.2502

M at 1.8 MPa gives  A/A* = 1.4390

Therefore, by interpolation, we have M = 1.75 MPa  gives A

However, we shall use M = 1.75 MPa and A

Similarly,

P/P₀ = 0.1878

a) Where the nozzle is choked at the throat there is subsonic flow in the following diverging part of the nozzle. From tables, we have

A/A* = 1.387. by interpolation M

Therefore P = P₀ × P

Which shows that the nozzle is choked for back pressures lower than 4.279 MPa

b) Where there is a normal shock at the exit of the nozzle, we have;

M₁ = 1.75 MPa, P₁ = 0.1878 × 5 = 0.939 MPa

Where the normal shock is at M₁ = 1.75 MPa, P₂/P₁ = 3.406

Where the normal shock occurs at the nozzle exit, we have

Where the shock occurs t the section prior to the nozzle exit from the throat, the back pressure was derived as = 4.279 MPa

Therefore the back pressure value ranges from 3.198 MPa to 4.279 MPa

c) At M = 1.75 MPa  and P

d) Where the back pressure is less than 3.198 MPa according to isentropic flow relations supersonic flow will exist at the exit plane