Page of equations from a 1953 NACA report

This is from page 6 of NACA Report 1135 (1953). On the left is the scan, on the right is what we made from it.

The scan already came with a text layer, but it is unreadable. Open the box under the scan to see what a screen reader was reading aloud before.

The scan

Scan of equations 47 to 51. The same equations are written out on the right.
What a screen reader was reading before
_q--2 MS___--7 M 2 [therm peril p 2 pt 2 7 1o / MS\ -1 =.'(:+_-) .... M_\ -1 6M25 l "-k--_-) V'_ 2 7--1 (1 +_ M,,) -1 V:J = _- M_ M s / M2\ -' =_-kl+_-) [isen, peril [adiab, peril [adiab, peril [adiab, peril (47) (48) (49) (50) (51)

What we made

qp=γ2M2=710M2\frac{q}{p}=\frac{\gamma}{2}M^2=\frac{7}{10}M^2[therm perf](47)
qpt=γ2M2(1+γ−12M2)−γγ−1=710M2(1+M25)−72\frac{q}{p_t}=\frac{\gamma}{2}M^2\left(1+\frac{\gamma-1}{2}M^2\right)^{-\frac{\gamma}{\gamma-1}}=\frac{7}{10}M^2\left(1+\frac{M^2}{5}\right)^{-\frac{7}{2}}[isen, perf](48)
(Vat)2=M2(1+γ−12M2)−1=M2(1+M25)−1\left(\frac{V}{a_t}\right)^2=M^2\left(1+\frac{\gamma-1}{2}M^2\right)^{-1}=M^2\left(1+\frac{M^2}{5}\right)^{-1}[adiab, perf](49)
(Va∗)2=γ+12M2(1+γ−12M2)−1=6M25(1+M25)−1\left(\frac{V}{a_*}\right)^2=\frac{\gamma+1}{2}M^2\left(1+\frac{\gamma-1}{2}M^2\right)^{-1}=\frac{6M^2}{5}\left(1+\frac{M^2}{5}\right)^{-1}[adiab, perf](50)
(VVm)2=γ−12M2(1+γ−12M2)−1=M25(1+M25)−1\left(\frac{V}{V_m}\right)^2=\frac{\gamma-1}{2}M^2\left(1+\frac{\gamma-1}{2}M^2\right)^{-1}=\frac{M^2}{5}\left(1+\frac{M^2}{5}\right)^{-1}[adiab, perf](51)

We checked all 5. Each equation is written twice in the original, once in general form and once with the numbers for air plugged in, so we made sure both versions agree.

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