Pressure in a rotating body of liquid calculator

This online calculator allows you to calculate the pressure of a rotating body of liquid with a given density at a specified radius. Note that gravity is not accounted for and the pressure is relative to the pressure at r=0. See this forum post for more details on the formula.

[to-calculator-info][/to-calculator-info][calculator] [calculator-input name=“rho” label=“density” unit=“kg/m³”][/calculator-input] [calculator-input name=“n” label=“rotational frequency” unit=“Hz”][/calculator-input] [calculator-input name=“r” label=“radius” unit=“m”][/calculator-input]

[calculator-expression name=“w” formula=“2*PI*n” unit=“rad/s”] [calculator-expression name=“P” formula=“0.5*rho*w*w*r*r”]

[calculator-output name=“pressure” unit=“Pa”]A body of liquid rotating at <%= format(n, “Hz”) %> with density <%= format(rho, “kg/m³”) %> has a pressure of <%= format(P, “Pa”) %> (= <%= format(P/1e5, “bar”) %>) at a radius of <%= format(r, “m”) %> [/calculator-output]

[/calculator]

$$\omega = 2\cdot\pi\cdot n[Hz]$$$$P = \frac{1}{2}\cdot\rho\cdot\omega²\cdot r²$$