Convert knot to inch / hour
Learn how to convert
1
knot to
inch / hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(knot\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(knot\right) = {\color{rgb(89,182,91)} \dfrac{1852.0}{3.6 \times 10^{3}}\left(\dfrac{meter}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{1852.0}{3.6 \times 10^{3}}\left(\dfrac{m}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{inch}{hour}\right) = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}\left(\dfrac{meter}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}\left(\dfrac{m}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(knot\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1852.0}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1852.0}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1852.0}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1852.0}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{1852.0}{{\color{rgb(255,204,153)} \cancel{3.6}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{{\color{rgb(255,204,153)} \cancel{3.6}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}}\)
\(\text{Simplify}\)
\(1852.0 = {\color{rgb(20,165,174)} x} \times 2.54 \times 10^{-2}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.54 \times 10^{-2} = 1852.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.54 \times 10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.54 \times 10^{-2} \times \dfrac{1.0}{2.54 \times 10^{-2}} = 1852.0 \times \dfrac{1.0}{2.54 \times 10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = 1852.0 \times \dfrac{1.0}{2.54 \times 10^{-2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1852.0}{2.54 \times 10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 1852.0}{2.54}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx72913.385827\approx7.2913 \times 10^{4}\)
\(\text{Conversion Equation}\)
\(1.0\left(knot\right)\approx{\color{rgb(20,165,174)} 7.2913 \times 10^{4}}\left(\dfrac{inch}{hour}\right)\)
