Convert liter / second to gallon / second
Learn how to convert
1
liter / second to
gallon / second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{liter}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gallon}{second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{cubic \text{ } meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{liter}{second}\right) = {\color{rgb(89,182,91)} 10^{-3}\left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(89,182,91)} 10^{-3}\left(\dfrac{m^{3}}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gallon}{second}\right) = {\color{rgb(125,164,120)} 4.54609 \times 10^{-3}\left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(125,164,120)} 4.54609 \times 10^{-3}\left(\dfrac{m^{3}}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{liter}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gallon}{second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-3}} \times {\color{rgb(89,182,91)} \left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 4.54609 \times 10^{-3}}} \times {\color{rgb(125,164,120)} \left(\dfrac{cubic \text{ } meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m^{3}}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 4.54609 \times 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m^{3}}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m^{3}}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 4.54609 \times 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m^{3}}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-3} = {\color{rgb(20,165,174)} x} \times 4.54609 \times 10^{-3}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancel{10^{-3}}} = {\color{rgb(20,165,174)} x} \times 4.54609 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 4.54609\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 4.54609 = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{4.54609}\right)\)
\({\color{rgb(20,165,174)} x} \times 4.54609 \times \dfrac{1.0}{4.54609} = \times \dfrac{1.0}{4.54609}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{4.54609}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{4.54609}}} = \dfrac{1.0}{4.54609}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{4.54609}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.2199692483\approx2.1997 \times 10^{-1}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{liter}{second}\right)\approx{\color{rgb(20,165,174)} 2.1997 \times 10^{-1}}\left(\dfrac{gallon}{second}\right)\)
