Navier–Stokes equation with kinematic quantities

  
    
      
        
          
            
              ∂
              u
            
            
              ∂
              t
            
          
        
        +
        (
        u
        ∇
        )
        u
        =
        −
        ∇
        P
        +
        ν
        
          ∇
          
            2
          
        
        u
        .
{\displaystyle p={\frac {F\cdot {\text{distance}}}{A\cdot {\text{distance}}}}={\frac {\text{Work}}{\text{Volume}}}={\frac {\text{Energy (J)}}{{\text{Volume }}({\text{m}}^{3})}}.} Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in most other fields, except aviation where the hecto- prefix is commonly used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because pressure in the ocean increases by approximately one decibar per metre depth. The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa.
Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., centimetres of water, millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercurys high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely.