Pressure change from displacement thickness in duct

Outside the boundary layers the core flow is accelerated, because the displacement thickness reduces the effective flow area. Apply continuity to the core, then Bernoulli. The pressure falls by about 55.7 Pa.

Assumptions

Air density $\rho = 1.23\ \text{kg/m}^3$. The flow in the core is frictionless and incompressible, so Bernoulli applies between sections 1 and 2.

  Section 1                  Section 2
  ----------------------     ----------------------
   U0 = 30 m/s uniform  -->    core U2 (faster)
  ----------------------     = boundary layer (d* = 0.9 mm)

Continuity (effective area)

At section 2 the effective flow area is reduced by $\delta^*$ on each wall:

$$A_{eff} = (76 - 2 \times 0.9)^2 = 74.2^2\ \text{mm}^2,\qquad A_1 = 76^2\ \text{mm}^2$$ $$U_0A_1 = U_2A_{eff} \;\Rightarrow\; U_2 = 30\left(\frac{76}{74.2}\right)^2 = 31.47\ \text{m/s}$$

Bernoulli (horizontal duct)

$$\begin{aligned} p_1 - p_2 &= \tfrac12\rho\,(U_2^2 - U_0^2) \\ &= \tfrac12(1.23)(31.47^2 - 30^2) = 55.7\ \text{Pa} \end{aligned}$$

Answer: $p_2 - p_1 = -55.7$ Pa, i.e. the pressure drops by about 55.7 Pa (about 5.7 mm of water) between sections 1 and 2.