Convert liter / hour to gill / minute
Learn how to convert
1
liter / hour to
gill / minute
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{liter}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gill}{minute}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{cubic \text{ } meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{liter}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{10^{-3}}{3.6 \times 10^{3}}\left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{10^{-3}}{3.6 \times 10^{3}}\left(\dfrac{m^{3}}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gill}{minute}\right) = {\color{rgb(125,164,120)} \dfrac{1.420653125 \times 10^{-4}}{60.0}\left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{1.420653125 \times 10^{-4}}{60.0}\left(\dfrac{m^{3}}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{liter}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gill}{minute}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{-3}}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{cubic \text{ } meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.420653125 \times 10^{-4}}{60.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{cubic \text{ } meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{-3}}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m^{3}}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.420653125 \times 10^{-4}}{60.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m^{3}}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{-3}}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m^{3}}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.420653125 \times 10^{-4}}{60.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m^{3}}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10^{-3}}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.420653125 \times 10^{-4}}{60.0}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{10^{-3}}}}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.420653125 \times {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-4}}}}{60.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.420653125 \times 10^{-1}}{60.0} = \dfrac{1.0}{3.6 \times 10^{3}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{60.0}{1.420653125 \times 10^{-1}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.420653125 \times 10^{-1}}{60.0} \times \dfrac{60.0}{1.420653125 \times 10^{-1}} = \dfrac{1.0}{3.6 \times 10^{3}} \times \dfrac{60.0}{1.420653125 \times 10^{-1}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.420653125}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}} \times {\color{rgb(166,218,227)} \cancel{60.0}}}{{\color{rgb(166,218,227)} \cancel{60.0}} \times {\color{rgb(255,204,153)} \cancel{1.420653125}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}}} = \dfrac{1.0 \times 60.0}{3.6 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{3}}} \times 1.420653125 \times {\color{rgb(255,204,153)} \cancel{10^{-1}}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{60.0}{3.6 \times 10^{2} \times 1.420653125}\)
Rewrite equation
\(\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2} \times 60.0}{3.6 \times 1.420653125}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.1173169324\approx1.1732 \times 10^{-1}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{liter}{hour}\right)\approx{\color{rgb(20,165,174)} 1.1732 \times 10^{-1}}\left(\dfrac{gill}{minute}\right)\)
