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Vertical Depth given Pressure at any point with Origin at Free Surface Formula

GoEquation of Free Surface of liquid Formula

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Height of Crack refers to the size of a flaw or crack in a material that can lead to catastrophic failure under a given stress. Check FAQs

h = \frac{P atm - P Abs + (\frac{y}{[g]}) \cdot (0.5 \cdot {(ω \cdot d r)}^{2})}{ω}

h - Height of Crack?P_atm - Atmospheric Pressure?P_Abs - Absolute Pressure?y - Specific Weight of Liquid?ω - Angular Velocity?d_r - Radial Distance from Central Axis?[g] - Gravitational acceleration on Earth?

Vertical Depth given Pressure at any point with Origin at Free Surface Example

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Here is how the Vertical Depth given Pressure at any point with Origin at Free Surface equation looks like with Values.

Here is how the Vertical Depth given Pressure at any point with Origin at Free Surface equation looks like with Units.

Here is how the Vertical Depth given Pressure at any point with Origin at Free Surface equation looks like.

912585.4012 = \frac{101325 - 100000 + (\frac{9.81}{9.8066}) \cdot (0.5 \cdot {(2 \cdot 0.5)}^{2})}{2}

912585.4012mm = \frac{101325Pa - 100000Pa + (\frac{9.81kN/m³}{9.8066m/s²}) \cdot (0.5 \cdot {(2rad/s \cdot 0.5m)}^{2})}{2rad/s}

912585.4012 = \frac{101325 - 100000 + (\frac{9.81}{9.8066}) \cdot (0.5 \cdot {(2 \cdot 0.5)}^{2})}{2}

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Vertical Depth given Pressure at any point with Origin at Free Surface Solution

Follow our step by step solution on how to calculate Vertical Depth given Pressure at any point with Origin at Free Surface?

FIRST Step Consider the formula

h = \frac{P atm - P Abs + (\frac{y}{[g]}) \cdot (0.5 \cdot {(ω \cdot d r)}^{2})}{ω}

Next Step Substitute values of Variables

∴

h = \frac{101325Pa - 100000Pa + (\frac{9.81kN/m³}{[g]}) \cdot (0.5 \cdot {(2rad/s \cdot 0.5m)}^{2})}{2rad/s}

Next Step Substitute values of Constants

∴

h = \frac{101325Pa - 100000Pa + (\frac{9.81kN/m³}{9.8066m/s²}) \cdot (0.5 \cdot {(2rad/s \cdot 0.5m)}^{2})}{2rad/s}

Next Step Convert Units

∴

h = \frac{101325Pa - 100000Pa + (\frac{9810N/m³}{9.8066m/s²}) \cdot (0.5 \cdot {(2rad/s \cdot 0.5m)}^{2})}{2rad/s}

Next Step Prepare to Evaluate

∴

h = \frac{101325 - 100000 + (\frac{9810}{9.8066}) \cdot (0.5 \cdot {(2 \cdot 0.5)}^{2})}{2}

Next Step Evaluate

∴

h = 912.585401232837m

Next Step Convert to Output's Unit

∴

h = 912585.401232837mm

LAST Step Rounding Answer

∴

h = 912585.4012mm

Vertical Depth given Pressure at any point with Origin at Free Surface Formula Elements

Variables

Constants

Height of Crack

Height of Crack refers to the size of a flaw or crack in a material that can lead to catastrophic failure under a given stress.

Symbol: h

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Height of Crack

Atmospheric Pressure

Atmospheric pressure, also known as barometric pressure, is the pressure within the atmosphere of Earth.

Symbol: P_atm

Measurement: PressureUnit: Pa