Mechanical Properties of Fluids

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Hydrostatic pressure is given by: $$ P = P_{\text{atm}} + \rho g h $$ Where: - $ P $ = absolute pressure at depth $ h $ - $ P_{\text{atm}} $ = atmospheric pressure ($ 1.01 \times 10^5 \, \text{Pa} …

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Given: - $ h = 1500 \, \text{m} $ - $ \rho = 1024 \, \text{kg/m}^3 $ - $ g = 9.80 \, \text{m/s}^2 $ - $ P_{\text{atm}} = 1.01 \times 10^5 \, \text{Pa} $ Formula: $ P = P_{\text{atm}} + \rho g h $ St…

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Because hydrostatic pressure increases linearly with depth ($ P \propto h $). The deeper the water, the greater the pressure exerted on the dam wall. To withstand this increasing pressure, the wall mu…

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Pascal's Law states that when pressure is applied to an enclosed fluid, it is transmitted undiminished to every part of the fluid and to the walls of the container. This means that a small force appl…

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Given: - $ F_1 = 500 \, \text{N} $ - $ A_1 = 0.02 \, \text{m}^2 $ - $ A_2 = 1.5 \, \text{m}^2 $ By Pascal’s Law: $ \frac{F_1}{A_1} = \frac{F_2}{A_2} $ Step 1: $ \frac{500}{0.02} = \frac{F_2}{1.5} $ …

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Given: - $ m_1 = 25 \, \text{kg} \Rightarrow F_1 = 25 \times 9.8 = 245 \, \text{N} $ - $ A_1 = 0.05 \, \text{m}^2 $ - $ A_2 = 10 \, \text{m}^2 $ Using Pascal’s Law: $ \frac{F_1}{A_1} = \frac{F_2}{A_2…

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Surface tension is the property of a liquid's surface that allows it to resist external force. It is defined as the force per unit length acting perpendicular to an imaginary line on the surface. $$ …

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Due to surface tension. A sphere has the smallest surface area for a given volume. The liquid surface tends to minimize its area due to cohesive forces between molecules, resulting in a spherical shap…