Time of Emptying Hemispherical Tank Calculator

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Orifices and Mouthpieces

Draft Tube

Properties of Surfaces and Solids

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✖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.ⓘ Hemispherical Tank Radius [R_t]			+10% -10%
✖The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom.ⓘ Initial Height of Liquid [H_i]			+10% -10%
✖The Final height of liquid is a variable from the tank emptying through an orifice at its bottom.ⓘ Final Height of Liquid [H_f]			+10% -10%
✖The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge.ⓘ Coefficient of Discharge [C_d]			+10% -10%
✖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).ⓘ Area of Orifice [a]			+10% -10%

✖Total Time Taken is the total time taken by the body to cover that space.ⓘ Time of Emptying Hemispherical Tank [t_total]

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Formula

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Time of Emptying Hemispherical Tank

Formula

`"t"_{"total"} = (pi*(((4/3)*"R"_{"t"}*(("H"_{"i"}^1.5)-("H"_{"f"}^1.5)))-(0.4*(("H"_{"i"}^(5/2))-("H"_{"f"})^(5/2)))))/("C"_{"d"}*"a"*(sqrt(2*9.81)))`

Example

`"12.99151s"=(pi*(((4/3)*"15m"*((("24m")^1.5)-(("20.1m")^1.5)))-(0.4*((("24m")^(5/2))-("20.1m")^(5/2)))))/("0.87"*"9.1m²"*(sqrt(2*9.81)))`

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Time of Emptying Hemispherical Tank Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
t_total = (pi*(((4/3)*R_t*((H_i^1.5)-(H_f^1.5)))-(0.4*((H_i^(5/2))-(H_f)^(5/2)))))/(C_d*a*(sqrt(2*9.81)))
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Total Time Taken - (Measured in Second) - Total Time Taken is the total time taken by the body to cover that space.
Hemispherical Tank Radius - (Measured in Meter) - 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.
Initial Height of Liquid - (Measured in Meter) - The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom.
Final Height of Liquid - (Measured in Meter) - The Final height of liquid is a variable from the tank emptying through an orifice at its bottom.
Coefficient of Discharge - The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge.
Area of Orifice - (Measured in Square Meter) - 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).

STEP 1: Convert Input(s) to Base Unit

Hemispherical Tank Radius: 15 Meter --> 15 Meter No Conversion Required
Initial Height of Liquid: 24 Meter --> 24 Meter No Conversion Required
Final Height of Liquid: 20.1 Meter --> 20.1 Meter No Conversion Required
Coefficient of Discharge: 0.87 --> No Conversion Required
Area of Orifice: 9.1 Square Meter --> 9.1 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_total = (pi*(((4/3)*R_t*((H_i^1.5)-(H_f^1.5)))-(0.4*((H_i^(5/2))-(H_f)^(5/2)))))/(C_d*a*(sqrt(2*9.81))) --> (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)))

Evaluating ... ...

t_total = 12.9915096894501

STEP 3: Convert Result to Output's Unit

12.9915096894501 Second --> No Conversion Required

FINAL ANSWER

12.9915096894501 ≈ 12.99151 Second <-- Total Time Taken

(Calculation completed in 00.004 seconds)

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Home » Physics » Fluid Mechanics » Orifices and Mouthpieces » Velocity and Time » Time of Emptying Hemispherical Tank

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PSG College of Technology (PSGCT), Coimbatore

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Amrita School of Engineering (ASE), Vallikavu

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< 8 Velocity and Time Calculators

Time of Emptying Hemispherical Tank

Go 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)))

Time of Emptying Circular Horizontal Tank

Go Total Time Taken = (4*Length*((((2*Radius 1)-Final Height of Liquid)^(3/2))-((2*Radius 1)-Initial Height of Liquid)^(3/2)))/(3*Coefficient of Discharge*Area of Orifice*(sqrt(2*9.81)))

Time of Emptying Tank through Orifice at Bottom

Go 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))

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

Go Velocity of Liquid Inlet = sqrt(2*9.81*(Atmospheric Pressure Head+Constant Head-Absolute Pressure Head))

Coefficient of velocity for horizontal and vertical distance

Go Coefficient of Velocity = Horizontal Distance/(sqrt(4*Vertical Distance*Head of the Liquid))

Coefficient of Velocity given Head Loss

Go Coefficient of Velocity = sqrt(1-(Head Loss/Head of the Liquid))

Coefficient of velocity

Go Coefficient of Velocity = Actual Velocity/Theoretical Velocity

Theoretical velocity

Go Velocity = sqrt(2*9.81*Pelton Head)

Time of Emptying Hemispherical Tank Formula

What is 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.

What is coefficient of discharge?

The coefficient of discharge is defined as the ratio of the actual discharge from an orifice to the theoretical discharge from the orifice.

How to Calculate Time of Emptying Hemispherical Tank?

Time of Emptying Hemispherical Tank calculator 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 calculate 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 calculate Time of Emptying Hemispherical Tank using this online calculator? To use this online calculator 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. Here is how the Time of Emptying Hemispherical Tank calculation can be explained with given input values -> 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))).

FAQ

What is Time of Emptying Hemispherical Tank?

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 and is represented as t_total = (pi*(((4/3)*R_t*((H_i^1.5)-(H_f^1.5)))-(0.4*((H_i^(5/2))-(H_f)^(5/2)))))/(C_d*a*(sqrt(2*9.81))) or 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))). 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, The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom, The Final height of liquid is a variable from the tank emptying through an orifice at its bottom, The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge & 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).

How to calculate Time of Emptying Hemispherical Tank?

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 is calculated using 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 calculate Time of Emptying Hemispherical Tank, you need 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). With our tool, you need to enter the respective value for Hemispherical Tank Radius, Initial Height of Liquid, Final Height of Liquid, Coefficient of Discharge & Area of Orifice and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Total Time Taken?

In this formula, Total Time Taken uses Hemispherical Tank Radius, Initial Height of Liquid, Final Height of Liquid, Coefficient of Discharge & Area of Orifice. We can use 2 other way(s) to calculate the same, which is/are as follows -

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 1)-Final Height of Liquid)^(3/2))-((2*Radius 1)-Initial Height of Liquid)^(3/2)))/(3*Coefficient of Discharge*Area of Orifice*(sqrt(2*9.81)))

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