Unit Conversion
Understanding unit conversion is essential in pressure calculations. Here, it's necessary to convert the pressure from \(N/cm^2\) to \(N/m^2\), a more commonly used unit. Why do we convert units? This standardizes measurements, making them easier to work with and understand in different contexts. - 1 meter (m) equals 100 centimeters (cm)- To convert from \(N/cm^2\) to \(N/m^2\), use the conversion factor of \(100^2\) because there are \(100 \, cm\) in a \(meter\)- Thus, \(30 \, N/cm^2 \, becomes \, 300000 \, N/m^2\) after conversion. This process helps simplify pressure calculations, providing a standard unit that's widely understood.
Pressure Reduction
Pressure reduction involves calculating how much pressure decreases from its original value. In this problem, the pressure is reduced by \(\frac{7}{100}\) or 7% of its initial value. Here’s how to think about it: - Identify the percentage of reduction, which is \(7\%\) in this case - Multiply this percentage by the initial pressure value to find the decrease For example, if the original pressure is \(300000 \, N/m^2\), a 7% reduction means calculating \(\frac{7}{100} \, of \, 300000\). This equates to a decrease of \(21000 \, N/m^2\). Understanding pressure reduction helps in determining the new or resulting pressure efficiently.
Resulting Pressure
Once you know the decrease in pressure, finding the resulting (or new) pressure is straightforward. You simply subtract the reduced amount from the original pressure: - Original pressure: \(300000 \, N/m^2\)- Decrease in pressure: \(21000 \, N/m^2\) - Resulting pressure: \(300000 \, - \, 21000 = 279000 \, N/m^2\) This subtraction gives the resulting pressure, \(279000 \, N/m^2\), which is the pressure inside the vessel after the change. This step is critical in situations where pressure adjustments are necessary, such as in mechanical systems, fluid dynamics, or various engineering applications.
N/cm² to N/m² Conversion
Converting from \(N/cm^2\) to \(N/m^2\) is a key skill when dealing with pressure measurements. Here's why it's important and how it's done: - \(1 \, m \, = \, 100 \, cm\). Therefore, to convert areas from \(cm^2\) to \(m^2\), multiply by \(100^2\) - \(30 \, N/cm^2 \, \rightarrow \, 30 \, N/cm^2 \, \times \, 10,000 \, cm^2 \, / \, m^2 \, = \, 300,000 \, N/m^2\) Converting these units is not just a formulaic step, but it helps in visualizing and simplifying calculations with standard scientific units, ensuring consistency in problem-solving and data representation.
