Q23PE - College Physics (Urone)

Question

Convert an absolute pressure of 7 x 10⁵ N/M² to gauge pressure in lb/in²  (This value was stated to be just less than 90.0 lb/in² in Example 13.9. Is it?)

Step-by-Step Solution

Answer

Pressure in terms of lb/in² is 86.95 lb/in².

Step 1: Introduction

We use conversion units to convert N to lb and meters to inches.

Step 2: Given parameters and conversion units

Absolute pressure =  7 x 10⁵ N/M² 

gauge pressure = 5.99 x 10⁵ N/m² 

1 N = 0.225 lb

1 meter = 39.37 inches

Step 3: Calculate the pressure in new units

$\begin{array}{rcl}\mathbf{5}\mathbf{.}\mathbf{99}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}\mathbf{N}\mathbf{/}{\mathbf{m}}^{\mathbf{2}}& \mathbf{=}& \frac{\mathbf{5}\mathbf{.}\mathbf{99}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{225}}{\mathbf{39}\mathbf{.}\mathbf{37}\mathbf{\times }\mathbf{39}\mathbf{.}\mathbf{37}}\mathbf{lb}\mathbf{/}{\mathbf{in}}^{\mathbf{2}}\\ & \mathbf{=}& \mathbf{86}\mathbf{.}\mathbf{95}\mathbf{ }\mathbf{lb}\mathbf{/}{\mathbf{in}}^{\mathbf{2}}\end{array}$

Therefore, the pressure in new units is 86.95 lb/in² which was stated as just less than 90 lb/in².