Convert liter / minute to gallon / hour
Learn how to convert
1
liter / minute to
gallon / hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{liter}{minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gallon}{hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{cubic \text{ } meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{liter}{minute}\right) = {\color{rgb(89,182,91)} \dfrac{10^{-3}}{60.0}\left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{10^{-3}}{60.0}\left(\dfrac{m^{3}}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gallon}{hour}\right) = {\color{rgb(125,164,120)} \dfrac{4.40488377086 \times 10^{-3}}{3.6 \times 10^{3}}\left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{4.40488377086 \times 10^{-3}}{3.6 \times 10^{3}}\left(\dfrac{m^{3}}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{liter}{minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gallon}{hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{-3}}{60.0}} \times {\color{rgb(89,182,91)} \left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{4.40488377086 \times 10^{-3}}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{cubic \text{ } meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{-3}}{60.0}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m^{3}}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{4.40488377086 \times 10^{-3}}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m^{3}}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{-3}}{60.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m^{3}}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{4.40488377086 \times 10^{-3}}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m^{3}}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10^{-3}}{60.0} = {\color{rgb(20,165,174)} x} \times \dfrac{4.40488377086 \times 10^{-3}}{3.6 \times 10^{3}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{10^{-3}}}}{60.0} = {\color{rgb(20,165,174)} x} \times \dfrac{4.40488377086 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}}{3.6 \times 10^{3}}\)
\(\text{Simplify}\)
\(\dfrac{1.0}{60.0} = {\color{rgb(20,165,174)} x} \times \dfrac{4.40488377086}{3.6 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{4.40488377086}{3.6 \times 10^{3}} = \dfrac{1.0}{60.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.6 \times 10^{3}}{4.40488377086}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{4.40488377086}{3.6 \times 10^{3}} \times \dfrac{3.6 \times 10^{3}}{4.40488377086} = \dfrac{1.0}{60.0} \times \dfrac{3.6 \times 10^{3}}{4.40488377086}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{4.40488377086}} \times {\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}}}{{\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{4.40488377086}}} = \dfrac{1.0 \times 3.6 \times 10^{3}}{60.0 \times 4.40488377086}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{3.6 \times 10^{3}}{60.0 \times 4.40488377086}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx13.621244764\approx13.6212\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{liter}{minute}\right)\approx{\color{rgb(20,165,174)} 13.6212}\left(\dfrac{gallon}{hour}\right)\)
