To determine the pressure exerted by a column of water 100 cm high, we can utilize the concept of pressure and the given information. The pressure exerted by a column of fluid is directly proportional to the height of the column and the density of the fluid. In this case, we are dealing with water, which has a known density of 1000 kg/m³.
First, let’s convert the height of the column from centimeters to meters. Since there are 100 centimeters in a meter, the height of the column in meters is 100 cm / 100 = 1 meter.
Now, we can calculate the pressure using the formula:
Pressure = density × gravitational acceleration × height
Given that the density of water is 1000 kg/m³ and the gravitational acceleration is approximately 9.8 m/s², we can substitute these values into the formula:
Pressure = 1000 kg/m³ × 9.8 m/s² × 1 meter
Calculating this equation, we find that the pressure exerted by a column of water 100 cm high is approximately 9800 pascals (Pa).
To put this into perspective, the pressure is equivalent to approximately 0.098 atmospheres (atm) or 0.96 kilograms per square centimeter (kg/cm²). This means that every square meter at the base of the column is experiencing a force of 9800 newtons pushing down on it.
In practical terms, this pressure is relatively low and not particularly significant in most everyday situations. However, it is important to keep in mind that the pressure increases with the height of the column, as well as with the density of the fluid. Therefore, in taller columns or denser fluids, the pressure exerted can be much higher.
Understanding the pressure exerted by a column of water is valuable in various fields, such as engineering, hydrology, and plumbing. It helps us comprehend the forces involved in fluid systems and design structures accordingly.