Final answer:
By analyzing the constituent units of height (m), density (kg/m³), and gravitational acceleration (m/s²), the product hrhog has the SI unit of pressure, N/m². Hence, hrhog is correctly expressed in newtons per square meter, confirming the SI unit for pressure.
Step-by-step explanation:
To verify that the SI unit of hrhog is N/m2, let's break down each component of the given expression. The variable h represents height or depth, and is measured in meters (m). The Greek letter rho (often written as 'rh') denotes density, typically expressed in kilograms per cubic meter (kg/m3).
The letter g stands for the acceleration due to gravity, which is a constant with a value approximately equal to 9.8 meters per second squared (m/s2).
Combining these units, we have:
When multiplied together, they yield:
h*rho*g = m * (kg/m3) * (m/s2) = kg * m2 / s2 * m-3 = kg/(s2 * m) = N/m2
Since 1 N (Newton) is defined as the force that produces an acceleration of 1 m/s2 on a 1 kg mass, it is equivalent to kg * m/s2. Therefore, we can confirm that hrhog indeed has the SI unit of pressure, which is Newtons per square meter (N/m2).