Question

The wall thickness is equal to $\Delta r=1.0mm$ and the radius of the tube and the flask equals $r=25mm$. What internal pressure (in the absence of an external pressure) can be sustained by a glass tube?

• A. $20atm$
  
• B. $25atm$
• C. $30atm$
• D. $50atm$

Answer 1

The correct option is A $20atm$

Let the length of glass tube $l$ mm

Area of cross section of wall = $\Delta r\left(2l\right)$

Area of the cross section through axis = $2rl$

Inward elastic force = $Area\times stress$

= $\Delta r\left(2l\right)\times \sigma$

Outward force = $p\times 2rl$

Balancing the forces we have

$\Delta r\left(2l\right)\times \sigma$ = $p\times 2rl$

$p=\frac{\Delta r\times \sigma }{r}$

= $1\times {10}^{-3}\times 5\times {10}^7/25\times {10}^{-3}$

= $20\times {10}^5$ pascals

= $20$ atm