First slide

Pressure in a fluid-mechanical properties of fluids

Question

A tube of uniform cross-section has two vertical portions connected with a horizontal thin tube 8 cm long at their lower ends. Enough water to occupy 22 cm of the tube is poured into one branch and enough oil of specific gravity 0.8 to occupy 22 cm is poured into the other. Find the distance (in cm) of the common surface E of the two liquids from point B.

Moderate

Solution

$\begin{array}{l} h_{w} + 8 cm + h_{0} = 22 cm + 22 cm \\ \Rightarrow h_{w} + h_{0} = 36 cm \\ P_{C} = P_{B} \Rightarrow h_{0} ρ_{0} g = h_{w} ρ_{0} g \Rightarrow h_{0} \times 0.8 = h_{w} \times 1 \\ \Rightarrow h_{0} = \frac{h_{w}}{0.8} = 1.25 h_{w} \Rightarrow h_{w} + 1.25 h_{w} = 36 \\ \Rightarrow h_{w} = \frac{36}{2.25} = 16 cm \Rightarrow B E = 22 - 16 = 6 cm \end{array}$

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