Convert cubic meter / minute to gallon / hour

Learn how to convert 1 cubic meter / minute to gallon / hour step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{c u b i c m e t e r}{m i n u t e}) = x (\frac{g a l l o n}{h o u r})

Define the base values of the selected units in relation to the SI unit

(\frac{c u b i c m e t e r}{s e c o n d})

Left side: 1.0 (\frac{c u b i c m e t e r}{m i n u t e}) = \frac{1.0}{60.0} (\frac{c u b i c m e t e r}{s e c o n d}) = \frac{1.0}{60.0} (\frac{m^{3}}{s})

Right side: 1.0 (\frac{g a l l o n}{h o u r}) = \frac{4.54609 \times 10^{- 3}}{3.6 \times 10^{3}} (\frac{c u b i c m e t e r}{s e c o n d}) = \frac{4.54609 \times 10^{- 3}}{3.6 \times 10^{3}} (\frac{m^{3}}{s})

Insert known values into the conversion equation to determine

x

1.0 (\frac{c u b i c m e t e r}{m i n u t e}) = x (\frac{g a l l o n}{h o u r})

Insert known values =>

1.0 \times \frac{1.0}{60.0} \times (\frac{c u b i c m e t e r}{s e c o n d}) = x \times \frac{4.54609 \times 10^{- 3}}{3.6 \times 10^{3}} \times (\frac{c u b i c m e t e r}{s e c o n d})

Or

1.0 \cdot \frac{1.0}{60.0} \cdot (\frac{m^{3}}{s}) = x \cdot \frac{4.54609 \times 10^{- 3}}{3.6 \times 10^{3}} \cdot (\frac{m^{3}}{s})

Cancel SI units

1.0 \times \frac{1.0}{60.0} \cdot (\frac{m^{3}}{s}) = x \times \frac{4.54609 \times 10^{- 3}}{3.6 \times 10^{3}} \times (\frac{m^{3}}{s})

Conversion Equation

\frac{1.0}{60.0} = x \times \frac{4.54609 \times 10^{- 3}}{3.6 \times 10^{3}}

Switch sides

x \times \frac{4.54609 \times 10^{- 3}}{3.6 \times 10^{3}} = \frac{1.0}{60.0}

Isolate

x

Multiply both sides by

(\frac{3.6 \times 10^{3}}{4.54609 \times 10^{- 3}})

x \times \frac{4.54609 \times 10^{- 3}}{3.6 \times 10^{3}} \times \frac{3.6 \times 10^{3}}{4.54609 \times 10^{- 3}} = \frac{1.0}{60.0} \times \frac{3.6 \times 10^{3}}{4.54609 \times 10^{- 3}}

Cancel

x \times \frac{4.54609 \times 10^{- 3} \times 3.6 \times 10^{3}}{3.6 \times 10^{3} \times 4.54609 \times 10^{- 3}} = \frac{1.0 \times 3.6 \times 10^{3}}{60.0 \times 4.54609 \times 10^{- 3}}

Simplify

x = \frac{3.6 \times 10^{3}}{60.0 \times 4.54609 \times 10^{- 3}}

Rewrite equation

\frac{1.0}{10^{- 3}} can be rewritten to 10^{3}

Rewrite

x = \frac{10^{3} \times 3.6 \times 10^{3}}{60.0 \times 4.54609}

Simplify

x = \frac{10^{6} \times 3.6}{60.0 \times 4.54609}

Solve

x

x \approx 13198.154898 \approx 1.3198 \times 10^{4}

Conversion Equation

1.0 (\frac{c u b i c m e t e r}{m i n u t e}) \approx 1.3198 \times 10^{4} (\frac{g a l l o n}{h o u r})

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