Discussion
A pipe contains an oil of specific gravity 0.8. A differential manometer connected at two points A and B shows a difference in mercury (specific gravity 13.6) level as 10 cm. The difference of pressure at two points (in N/m2 ) is :
* Consider acceleration due to gravity as 10 m/s2.
Answer: A
The pressure difference is \(12800\ N/m^{2}\).
For a differential manometer with mercury below a lighter liquid, the pressure difference is the head of mercury less the equal head of the pipe liquid it displaces.
\[ \begin{aligned} \Delta p &= g h (\rho_{Hg} - \rho_{oil}) \\ &= 10 \times 0.1 \times (13600 - 800) \\ &= 12800\ N/m^{2} \end{aligned} \]
13600 forgets to subtract the oil column, and 1280 and 1360 are the same figures with a factor of ten slip in the 10 cm head.
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