Convert liter / second to gallon / hour

Learn how to convert 1 liter / second to gallon / hour step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(\dfrac{liter}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gallon}{hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{cubic \text{ } meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{liter}{second}\right) = {\color{rgb(89,182,91)} 10^{-3}\left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(89,182,91)} 10^{-3}\left(\dfrac{m^{3}}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gallon}{hour}\right) = {\color{rgb(125,164,120)} \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}\left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}\left(\dfrac{m^{3}}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{liter}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gallon}{hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-3}} \times {\color{rgb(89,182,91)} \left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{cubic \text{ } meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m^{3}}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m^{3}}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m^{3}}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m^{3}}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-3} = {\color{rgb(20,165,174)} x} \times \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancel{10^{-3}}} = {\color{rgb(20,165,174)} x} \times \dfrac{4.54609 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}}{3.6 \times 10^{3}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{4.54609}{3.6 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{4.54609}{3.6 \times 10^{3}} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.6 \times 10^{3}}{4.54609}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{4.54609}{3.6 \times 10^{3}} \times \dfrac{3.6 \times 10^{3}}{4.54609} = \times \dfrac{3.6 \times 10^{3}}{4.54609}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{4.54609}} \times {\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}}}{{\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{4.54609}}} = \dfrac{3.6 \times 10^{3}}{4.54609}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{3.6 \times 10^{3}}{4.54609}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx791.88929388\approx7.9189 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{liter}{second}\right)\approx{\color{rgb(20,165,174)} 7.9189 \times 10^{2}}\left(\dfrac{gallon}{hour}\right)\)

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