Final answer:
The pressure at a depth of 10 meters for a fluid with a density of 1152 kg/m³ can be calculated using the hydrostatic pressure formula. By inserting the values for depth, density, and gravity into the formula, one can determine the resulting pressure in Pascals. This calculation assumes the fluid is incompressible.
Step-by-step explanation:
To find the pressure at a depth of 10 meters for a fluid with a density of 1152 kg/m³, we can use the hydrostatic pressure formula p = hρg. The variables in this formula are h (height or depth of the fluid column), ρ (density of the fluid), and g (acceleration due to gravity, which is approximately 9.81 m/s² on Earth). To perform the calculation, convert all variables to consistent units, and then apply the formula.
The depth h is already given in meters, so no conversion is needed. The density ρ = 1152 kg/m³ can be used directly. Plugging these values into the equation with the acceleration due to gravity, we obtain p = (10 m) × (1152 kg/m³) × (9.81 m/s²). Carrying out this multiplication gives us a pressure p which can then be expressed in Pascals (Pa), the standard SI unit for pressure.
It is important to note that this calculation assumes the fluid is incompressible and thus its density does not change significantly with depth, which is true for liquids like water.