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Time of Emptying Hemispherical Tank Formula

GoTime of Emptying Tank through Orifice at Bottom Formula

GoTime of Emptying Circular Horizontal Tank Formula

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

t total = \frac{π \cdot (((\frac{4}{3}) \cdot R t \cdot (({H i}^{1.5}) - ({H f}^{1.5}))) - (0.4 \cdot (({H i}^{\frac{5}{2}}) - {(H f)}^{\frac{5}{2}})))}{C d \cdot a \cdot (\sqrt{2 \cdot 9.81})}

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

Time of Emptying Hemispherical Tank Example

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

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

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

12.9915 = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15 \cdot ((24^{1.5}) - ({20.1}^{1.5}))) - (0.4 \cdot ((24^{\frac{5}{2}}) - {(20.1)}^{\frac{5}{2}})))}{0.87 \cdot 9.1 \cdot (\sqrt{2 \cdot 9.81})}

12.9915s = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15m \cdot (({24m}^{1.5}) - ({20.1m}^{1.5}))) - (0.4 \cdot (({24m}^{\frac{5}{2}}) - {(20.1m)}^{\frac{5}{2}})))}{0.87 \cdot 9.1m² \cdot (\sqrt{2 \cdot 9.81})}

12.9915 = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15 \cdot ((24^{1.5}) - ({20.1}^{1.5}))) - (0.4 \cdot ((24^{\frac{5}{2}}) - {(20.1)}^{\frac{5}{2}})))}{0.87 \cdot 9.1 \cdot (\sqrt{2 \cdot 9.81})}

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Time of Emptying Hemispherical Tank Solution

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

FIRST Step Consider the formula

t total = \frac{π \cdot (((\frac{4}{3}) \cdot R t \cdot (({H i}^{1.5}) - ({H f}^{1.5}))) - (0.4 \cdot (({H i}^{\frac{5}{2}}) - {(H f)}^{\frac{5}{2}})))}{C d \cdot a \cdot (\sqrt{2 \cdot 9.81})}

Next Step Substitute values of Variables

∴

t total = \frac{π \cdot (((\frac{4}{3}) \cdot 15m \cdot (({24m}^{1.5}) - ({20.1m}^{1.5}))) - (0.4 \cdot (({24m}^{\frac{5}{2}}) - {(20.1m)}^{\frac{5}{2}})))}{0.87 \cdot 9.1m² \cdot (\sqrt{2 \cdot 9.81})}

Next Step Substitute values of Constants

∴

t total = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15m \cdot (({24m}^{1.5}) - ({20.1m}^{1.5}))) - (0.4 \cdot (({24m}^{\frac{5}{2}}) - {(20.1m)}^{\frac{5}{2}})))}{0.87 \cdot 9.1m² \cdot (\sqrt{2 \cdot 9.81})}

Next Step Prepare to Evaluate

∴

t total = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15 \cdot ((24^{1.5}) - ({20.1}^{1.5}))) - (0.4 \cdot ((24^{\frac{5}{2}}) - {(20.1)}^{\frac{5}{2}})))}{0.87 \cdot 9.1 \cdot (\sqrt{2 \cdot 9.81})}

Next Step Evaluate

∴

t total = 12.9915096894501s

LAST Step Rounding Answer

∴

t total = 12.9915s

Time of Emptying Hemispherical Tank Formula Elements

Variables

Constants

Functions

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

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

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

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

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 to find Total Time Taken

Go Time of Emptying Tank through Orifice at Bottom

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

Go Time of Emptying Circular Horizontal Tank

t total = \frac{4 \cdot L \cdot (({((2 \cdot r 1) - H f)}^{\frac{3}{2}}) - {((2 \cdot r 1) - H i)}^{\frac{3}{2}})}{3 \cdot C d \cdot a \cdot (\sqrt{2 \cdot 9.81})}

Other formulas in Velocity and Time category

Go Theoretical velocity

v = \sqrt{2 \cdot 9.81 \cdot H p}

Go Velocity of liquid at C-C for Hc, Ha, and H

V i = \sqrt{2 \cdot 9.81 \cdot (H a + H c - H AP)}

Go Coefficient of velocity

C v = \frac{v a}{V th}

Go Coefficient of velocity for horizontal and vertical distance

C v = \frac{R}{\sqrt{4 \cdot V \cdot H}}

How to Evaluate Time of Emptying Hemispherical Tank?

Time of Emptying Hemispherical Tank evaluator uses Total Time Taken = (pi*(((4/3)*Hemispherical Tank Radius*((Initial Height of Liquid^1.5)-(Final Height of Liquid^1.5)))-(0.4*((Initial Height of Liquid^(5/2))-(Final Height of Liquid)^(5/2)))))/(Coefficient of Discharge*Area of Orifice*(sqrt(2*9.81))) to evaluate the Total Time Taken, The Time of Emptying Hemispherical Tank formula is known from while considering a hemispherical tank of radius R fitted with an orifice of area 'a' at its bottom. Total Time Taken is denoted by t_total symbol.

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

FAQs on Time of Emptying Hemispherical Tank

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

The formula of Time of Emptying Hemispherical Tank is expressed as Total Time Taken = (pi*(((4/3)*Hemispherical Tank Radius*((Initial Height of Liquid^1.5)-(Final Height of Liquid^1.5)))-(0.4*((Initial Height of Liquid^(5/2))-(Final Height of Liquid)^(5/2)))))/(Coefficient of Discharge*Area of Orifice*(sqrt(2*9.81))). Here is an example- 13.39064 = (pi*(((4/3)*15*((24^1.5)-(20.1^1.5)))-(0.4*((24^(5/2))-(20.1)^(5/2)))))/(0.87*9.1*(sqrt(2*9.81))).

How to calculate Time of Emptying Hemispherical Tank?

With Hemispherical Tank Radius (R_t), Initial Height of Liquid (H_i), Final Height of Liquid (H_f), Coefficient of Discharge (C_d) & Area of Orifice (a) we can find Time of Emptying Hemispherical Tank using the formula - Total Time Taken = (pi*(((4/3)*Hemispherical Tank Radius*((Initial Height of Liquid^1.5)-(Final Height of Liquid^1.5)))-(0.4*((Initial Height of Liquid^(5/2))-(Final Height of Liquid)^(5/2)))))/(Coefficient of Discharge*Area of Orifice*(sqrt(2*9.81))). This formula also uses Archimedes' constant and Square Root Function function(s).

What are the other ways to Calculate Total Time Taken?

Here are the different ways to Calculate Total Time Taken-

Total Time Taken=(2*Area of Tank*((sqrt(Initial Height of Liquid))-(sqrt(Final Height of Liquid))))/(Coefficient of Discharge*Area of Orifice*sqrt(2*9.81))
Total Time Taken=(4*Length*((((2*Radius)-Final Height of Liquid)^(3/2))-((2*Radius)-Initial Height of Liquid)^(3/2)))/(3*Coefficient of Discharge*Area of Orifice*(sqrt(2*9.81)))

Can the Time of Emptying Hemispherical Tank be negative?

Yes, the Time of Emptying Hemispherical Tank, measured in Time can be negative.

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

Time of Emptying Hemispherical Tank is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Time of Emptying Hemispherical Tank can be measured.

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Time of Emptying Hemispherical Tank Formula

​GoTime of Emptying Tank through Orifice at Bottom Formula

​GoTime of Emptying Circular Horizontal Tank Formula

Time of Emptying Hemispherical Tank Example

Time of Emptying Hemispherical Tank Solution

Time of Emptying Hemispherical Tank Formula Elements

Other Formulas to find Total Time Taken

Other formulas in Velocity and Time category

How to Evaluate Time of Emptying Hemispherical Tank?

FAQs on Time of Emptying Hemispherical Tank

Variable Name

GoTime of Emptying Tank through Orifice at Bottom Formula

GoTime of Emptying Circular Horizontal Tank Formula