The pressure in a compressed air storage tank is 1200 kPa . What is the tank's pressure in (a) k

step 1 1200 kilo Pascal Pascal is Newton per meter square so that equals 1200 kilo Newton per meter squ

The pressure in a compressed air storage tank is 1200 kPa ....

The pressure in a compressed air storage tank is $1200 \mathrm{kPa} .$ What is the tank's pressure in $(a) \mathrm{kN}$ and $\mathrm{m}$ units; (b) $\mathrm{kg}, \mathrm{m},$ and s units; and $(c) \mathrm{kg}, \mathrm{km},$ and s units?

Key Concepts

Dimensional Analysis

Dimensional analysis is a technique used to convert between different unit systems by ensuring that both sides of an equation have the same dimensional formula. This method helps verify the correctness of unit conversions by systematically tracking the dimensions (such as mass, length, and time) involved in derived units like pressure, ensuring the final expression in a chosen unit system is consistent with the physical quantity being measured.

Unit Conversion

Unit conversion involves changing a quantity expressed in one set of units to another set while preserving its value. This requires multiplication by appropriate conversion factors. For example, converting pressure from kilopascals (kPa) to kilonewtons per square meter (kN/m²) uses the fact that 1 kN equals 1000 N. Similarly, when converting to systems based on different representations of the fundamental meter unit, the conversion factors must account for the scale changes.

SI and Derived Units

The International System of Units (SI) uses base units such as kilograms (kg), meters (m), and seconds (s). Derived units like the Newton (N) and Pascal (Pa) are constructed from these base units. Specifically, 1 N is equivalent to 1 kg·m/s² and 1 Pa is 1 N/m², which can also be expressed directly in base units as kg/(m·s²).

Pressure

Pressure is a measure of force distributed over a unit area. It quantifies how much force is exerted per unit area, and its standard SI unit is the Pascal (Pa), which is defined as one Newton per square meter (N/m²). This concept is central in fluid mechanics and many engineering applications.

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