1. **Stating the problem:** We want to understand and use the formulas related to relative density (specific gravity), density, pressure, and head in fluid mechanics. 2. **Relative density (specific gravity) definition:** Relative density (RD) or specific gravity (SG) is the ratio of the density of a substance to the density of a reference substance (usually water at 4°C). $$\text{Relative density} = \frac{\text{density of substance } (\rho)}{1000 \text{ kg/m}^3}$$ 3. **Density from relative density:** Given relative density, we can find density by: $$\rho = \text{Relative density} \times 1000 \text{ kg/m}^3$$ 4. **Pressure formula:** Pressure due to a fluid column is given by: $$P = \rho g h$$ where: - $\rho$ is the density in kg/m³ - $g$ is acceleration due to gravity in m/s² - $h$ is the height of the fluid column in meters 5. **Units check:** $$\text{Pressure units} = (\text{kg/m}^3) \times (\text{m/s}^2) \times (\text{m}) = \text{kg/(m·s}^2) = \text{Pascal (Pa)}$$ 6. **Head formula:** The head (height of fluid column) can be found from pressure by: $$\text{Head} = \frac{P}{\rho g}$$ This means the height of the fluid column is the pressure divided by the product of density and gravitational acceleration. **Summary:** - Relative density relates density to water. - Pressure is calculated by multiplying density, gravity, and height. - Head is pressure divided by density and gravity. This explains the handwritten equation $P = \rho g h$ and the units $\text{kg/m}^3 \times \text{m/s}^2 \times \text{m}$ shown in the screenshot.