First slide

Pressure in a fluid-mechanical properties of fluids

Question

A tube with both ends open floats vertically in water. Oil with a density 800 kg/m³ is poured into the tube. The tube is filled with oil up to the top end while in equilibrium.
The portion out of the water is of length 10 cm. The length of the tube is:

Moderate

A

50 cm
B

60 cm
C

90 cm
D

100 cm

Solution

After oil is filled up, pressure at the depth of lower end should equate if measured from inside and outside the tube. Suppose depth of oil is x cm then:
$\begin{array}{l} 1000.g.[[(l - 10) cm] = 800 g . (x cm) + 1000 g [(l - x) cm] \\ \Rightarrow x = 50 cm \end{array}$
Now, pressure difference due to x cm depth of oil is equal to
pressure difference due to (l - x - l0) cm of water.
$\begin{array}{l} \Rightarrow 800 \cdot g \cdot x = 1000 g (l - 60) \\ \Rightarrow l = 100 cm \end{array}$

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