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My Physics Teacher wanted us to convert Pascal into Pound per Square Inch, not psi... he mentioned we'd use 9.8 m/s²... I'm not sure. I already did the simplest but it's not quite the answer: I used the unit psi 'cause I figured it's the same as pound per square inch (where I divided 1 lb/in² by 6894.75727 Pascals and multiply the quotient by the given Pascal unit which is 300) ... Our teacher must've required us to show the correct cancellations of units and the division plus multiplication, of course, to come up with the unit pound per square inch (lb/in²). The problem is, to avoid confusion, 300 Pa to lb/in².

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  • Your question is unclear to me. Please include a clear question. I suggest that you post this question in https://physics.stackexchange.com/ – NoChance Aug 15 '19 at 09:58
  • psi is pounds per square inch but it sound like your teacher wanted you to derive the conversion factor from basic units and constants rather than look it up in a big table of conversion factors (or on the Internet). – David K Aug 15 '19 at 10:29

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$$ 1~\text{Pa} = 1~\frac{\text{N}}{\text{m}^2} = 0.2248~\frac{\text{lbf}}{\text{m}^2} $$ because $1~\text{N} \approx 0.2248$ pounds-force. Then $$ 0.2248~\frac{\text{lbf}}{\text{m}^2}=0.2248~\frac{\text{lbf}}{(1~\text{m})^2} = 0.2248~\frac{\text{lbf}}{\left(39.37~\text{in} \right)^2} \approx 1.4503 \cdot 10^{-4}~\frac{\text{lbf}}{\text{in}^2} $$ therefore, $1~\text{Pa} \approx 1.4503 \cdot 10^{-4}~\text{psi}$. In order to get $300~\text{Pa}$, multiply both sides by $300$.

And what about the converting from Newton to pounds-force? We know that $$ 1~\text{lb} = 0.4536~\text{kg} \Rightarrow 1~\text{lbf} = 9.81~\frac{\text{m}}{\text{s}^2} \cdot 0.4536~\text{kg} \approx 4.448~\frac{\text{kg}\cdot \text{m}}{\text{s}^2} = 4.448~\text{N} $$ and therefore $$ 1~\text{lbf} = 4.448~\text{N}  \Rightarrow 1~\text{N} = \frac{1}{4.448}~\text{lbf} \approx 0.2248 ~\text{lbf} $$ Is it clear now?

Matti P.
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