Convert gallon / hour to liter / second
Learn how to convert
1
gallon / hour to
liter / second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{gallon}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{liter}{second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{cubic \text{ } meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{gallon}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}\left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}\left(\dfrac{m^{3}}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{liter}{second}\right) = {\color{rgb(125,164,120)} 10^{-3}\left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(125,164,120)} 10^{-3}\left(\dfrac{m^{3}}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{gallon}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{liter}{second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-3}}} \times {\color{rgb(125,164,120)} \left(\dfrac{cubic \text{ } meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m^{3}}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m^{3}}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m^{3}}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m^{3}}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{4.54609 \times 10^{-3}}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times 10^{-3}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{4.54609 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}\)
\(\text{Simplify}\)
\(\dfrac{4.54609}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x}\)
Switch sides
\({\color{rgb(20,165,174)} x} = \dfrac{4.54609}{3.6 \times 10^{3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 4.54609}{3.6}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0012628028\approx1.2628 \times 10^{-3}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{gallon}{hour}\right)\approx{\color{rgb(20,165,174)} 1.2628 \times 10^{-3}}\left(\dfrac{liter}{second}\right)\)
