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Area of Orifice given Time of Emptying Hemispherical Tank Formula

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The Area of Orifice is often a pipe or tube of varying cross-sectional area, and it can be used to direct or modify the flow of a fluid (liquid or gas). Check FAQs

a = \frac{π \cdot (((\frac{4}{3}) \cdot R t \cdot (({H i}^{\frac{3}{2}}) - ({H f}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot (({H i}^{\frac{5}{2}}) - {(H f)}^{\frac{5}{2}})))}{t total \cdot C d \cdot (\sqrt{2 \cdot 9.81})}

a - Area of Orifice?R_t - Hemispherical Tank Radius?H_i - Initial Height of Liquid?H_f - Final Height of Liquid?t_total - Total Time Taken?C_d - Coefficient of Discharge?π - Archimedes' constant?

Area of Orifice given Time of Emptying Hemispherical Tank Example

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Here is how the Area of Orifice given Time of Emptying Hemispherical Tank equation looks like with Values.

Here is how the Area of Orifice given Time of Emptying Hemispherical Tank equation looks like with Units.

Here is how the Area of Orifice given Time of Emptying Hemispherical Tank equation looks like.

3.9408 = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15 \cdot ((24^{\frac{3}{2}}) - ({20.1}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot ((24^{\frac{5}{2}}) - {(20.1)}^{\frac{5}{2}})))}{30 \cdot 0.87 \cdot (\sqrt{2 \cdot 9.81})}

3.9408m² = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15m \cdot (({24m}^{\frac{3}{2}}) - ({20.1m}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot (({24m}^{\frac{5}{2}}) - {(20.1m)}^{\frac{5}{2}})))}{30s \cdot 0.87 \cdot (\sqrt{2 \cdot 9.81})}

3.9408 = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15 \cdot ((24^{\frac{3}{2}}) - ({20.1}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot ((24^{\frac{5}{2}}) - {(20.1)}^{\frac{5}{2}})))}{30 \cdot 0.87 \cdot (\sqrt{2 \cdot 9.81})}

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Area of Orifice given Time of Emptying Hemispherical Tank Solution

Follow our step by step solution on how to calculate Area of Orifice given Time of Emptying Hemispherical Tank?

FIRST Step Consider the formula

a = \frac{π \cdot (((\frac{4}{3}) \cdot R t \cdot (({H i}^{\frac{3}{2}}) - ({H f}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot (({H i}^{\frac{5}{2}}) - {(H f)}^{\frac{5}{2}})))}{t total \cdot C d \cdot (\sqrt{2 \cdot 9.81})}

Next Step Substitute values of Variables

∴

a = \frac{π \cdot (((\frac{4}{3}) \cdot 15m \cdot (({24m}^{\frac{3}{2}}) - ({20.1m}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot (({24m}^{\frac{5}{2}}) - {(20.1m)}^{\frac{5}{2}})))}{30s \cdot 0.87 \cdot (\sqrt{2 \cdot 9.81})}

Next Step Substitute values of Constants

∴

a = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15m \cdot (({24m}^{\frac{3}{2}}) - ({20.1m}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot (({24m}^{\frac{5}{2}}) - {(20.1m)}^{\frac{5}{2}})))}{30s \cdot 0.87 \cdot (\sqrt{2 \cdot 9.81})}

Next Step Prepare to Evaluate

∴

a = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15 \cdot ((24^{\frac{3}{2}}) - ({20.1}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot ((24^{\frac{5}{2}}) - {(20.1)}^{\frac{5}{2}})))}{30 \cdot 0.87 \cdot (\sqrt{2 \cdot 9.81})}

Next Step Evaluate

∴

a = 3.94075793913321m²

LAST Step Rounding Answer

∴

a = 3.9408m²

Area of Orifice given Time of Emptying Hemispherical Tank Formula Elements

Variables

Constants

Functions

Area of Orifice

The Area of Orifice is often a pipe or tube of varying cross-sectional area, and it can be used to direct or modify the flow of a fluid (liquid or gas).

Symbol: a

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Orifice

Hemispherical Tank Radius

The Hemispherical tank radius is the distance from the center of a hemisphere to any point on the hemisphere is called the radius of the hemisphere.

Symbol: R_t

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Hemispherical Tank Radius

Initial Height of Liquid

The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom.

Symbol: H_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Initial Height of Liquid

Final Height of Liquid

The Final height of liquid is a variable from the tank emptying through an orifice at its bottom.

Symbol: H_f

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Final Height of Liquid

Total Time Taken

Total Time Taken is the total time taken by the body to cover that space.

Symbol: t_total

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Total Time Taken

Coefficient of Discharge

The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge.

Symbol: C_d

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Coefficient of Discharge

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Geometric Dimensions category

Go Vertical distance for coefficient of velocity and horizontal distance

V = \frac{R^{2}}{4 \cdot ({C v}^{2}) \cdot H}

Go Area of Tank given Time for Emptying Tank

A T = \frac{t total \cdot C d \cdot a \cdot (\sqrt{2 \cdot 9.81})}{2 \cdot ((\sqrt{H i}) - (\sqrt{H f}))}

Go Area at vena contracta for discharge and constant head

a c = \frac{Q M}{\sqrt{2 \cdot 9.81 \cdot H c}}

Go Area of Mouthpiece in Borda's Mouthpiece Running Full

A = \frac{Q M}{0.707 \cdot \sqrt{2 \cdot 9.81 \cdot H c}}

How to Evaluate Area of Orifice given Time of Emptying Hemispherical Tank?

Area of Orifice given Time of Emptying Hemispherical Tank evaluator uses Area of Orifice = (pi*(((4/3)*Hemispherical Tank Radius*((Initial Height of Liquid^(3/2))-(Final Height of Liquid^(3/2))))-((2/5)*((Initial Height of Liquid^(5/2))-(Final Height of Liquid)^(5/2)))))/(Total Time Taken*Coefficient of Discharge*(sqrt(2*9.81))) to evaluate the Area of Orifice, The Area of Orifice given Time of Emptying Hemispherical Tank is known from while considering a hemispherical tank of radius R fitted with an orifice of area 'a' at its bottom. Area of Orifice is denoted by a symbol.

How to evaluate Area of Orifice given Time of Emptying Hemispherical Tank using this online evaluator? To use this online evaluator for Area of Orifice given Time of Emptying Hemispherical Tank, enter Hemispherical Tank Radius (R_t), Initial Height of Liquid (H_i), Final Height of Liquid (H_f), Total Time Taken (t_total) & Coefficient of Discharge (C_d) and hit the calculate button.

FAQs on Area of Orifice given Time of Emptying Hemispherical Tank

What is the formula to find Area of Orifice given Time of Emptying Hemispherical Tank?

The formula of Area of Orifice given Time of Emptying Hemispherical Tank is expressed as Area of Orifice = (pi*(((4/3)*Hemispherical Tank Radius*((Initial Height of Liquid^(3/2))-(Final Height of Liquid^(3/2))))-((2/5)*((Initial Height of Liquid^(5/2))-(Final Height of Liquid)^(5/2)))))/(Total Time Taken*Coefficient of Discharge*(sqrt(2*9.81))). Here is an example- 4.061829 = (pi*(((4/3)*15*((24^(3/2))-(20.1^(3/2))))-((2/5)*((24^(5/2))-(20.1)^(5/2)))))/(30*0.87*(sqrt(2*9.81))).

How to calculate Area of Orifice given Time of Emptying Hemispherical Tank?

With Hemispherical Tank Radius (R_t), Initial Height of Liquid (H_i), Final Height of Liquid (H_f), Total Time Taken (t_total) & Coefficient of Discharge (C_d) we can find Area of Orifice given Time of Emptying Hemispherical Tank using the formula - Area of Orifice = (pi*(((4/3)*Hemispherical Tank Radius*((Initial Height of Liquid^(3/2))-(Final Height of Liquid^(3/2))))-((2/5)*((Initial Height of Liquid^(5/2))-(Final Height of Liquid)^(5/2)))))/(Total Time Taken*Coefficient of Discharge*(sqrt(2*9.81))). This formula also uses Archimedes' constant and Square Root Function function(s).

Can the Area of Orifice given Time of Emptying Hemispherical Tank be negative?

No, the Area of Orifice given Time of Emptying Hemispherical Tank, measured in Area cannot be negative.

Which unit is used to measure Area of Orifice given Time of Emptying Hemispherical Tank?

Area of Orifice given Time of Emptying Hemispherical Tank is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Orifice given Time of Emptying Hemispherical Tank can be measured.

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Area of Orifice given Time of Emptying Hemispherical Tank Formula

Area of Orifice given Time of Emptying Hemispherical Tank Example

Area of Orifice given Time of Emptying Hemispherical Tank Solution

Area of Orifice given Time of Emptying Hemispherical Tank Formula Elements

Other formulas in Geometric Dimensions category

How to Evaluate Area of Orifice given Time of Emptying Hemispherical Tank?

FAQs on Area of Orifice given Time of Emptying Hemispherical Tank

Variable Name