Coefficient of Discharge given Time of Emptying Hemispherical Tank Calculator

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Orifices and Mouthpieces

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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%
✖Total Time Taken is the total time taken by the body to cover that space.ⓘ Total Time Taken [t_total]			+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%

✖The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge.ⓘ Coefficient of Discharge given Time of Emptying Hemispherical Tank [C_d]

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Formula

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Coefficient of Discharge given Time of Emptying Hemispherical Tank

Formula

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

Example

`"0.376754"=(pi*(((4/3)*"15m"*((("24m")^(3/2))-(("20.1m")^(3/2))))-((2/5)*((("24m")^(5/2))-("20.1m")^(5/2)))))/("30s"*"9.1m²"*(sqrt(2*9.81)))`

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Coefficient of Discharge given Time of Emptying Hemispherical Tank Solution

STEP 0: Pre-Calculation Summary

Formula Used

Coefficient of Discharge = (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*Area of Orifice*(sqrt(2*9.81)))
C_d = (pi*(((4/3)*R_t*((H_i^(3/2))-(H_f^(3/2))))-((2/5)*((H_i^(5/2))-(H_f)^(5/2)))))/(t_total*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

Coefficient of Discharge - The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge.
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.
Total Time Taken - (Measured in Second) - Total Time Taken is the total time taken by the body to cover that space.
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
Total Time Taken: 30 Second --> 30 Second 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

C_d = (pi*(((4/3)*R_t*((H_i^(3/2))-(H_f^(3/2))))-((2/5)*((H_i^(5/2))-(H_f)^(5/2)))))/(t_total*a*(sqrt(2*9.81))) --> (pi*(((4/3)*15*((24^(3/2))-(20.1^(3/2))))-((2/5)*((24^(5/2))-(20.1)^(5/2)))))/(30*9.1*(sqrt(2*9.81)))

Evaluating ... ...

C_d = 0.376753780994054

STEP 3: Convert Result to Output's Unit

0.376753780994054 --> No Conversion Required

FINAL ANSWER

0.376753780994054 ≈ 0.376754 <-- Coefficient of Discharge

(Calculation completed in 00.004 seconds)

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Home » Physics » Fluid Mechanics » Orifices and Mouthpieces » Flow Rate » Coefficient of Discharge given Time of Emptying Hemispherical Tank

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< 11 Flow Rate Calculators

Discharge through partially sub-merged orifice

Go Discharge through Orifice = (Coefficient of Discharge*Width*(Height of Liquid Bottom Edge-Difference in Liquid Level)*(sqrt(2*9.81*Difference in Liquid Level)))+((2/3)*Coefficient of Discharge*Thickness of Dam*(sqrt(2*9.81))*((Difference in Liquid Level^1.5)-(Height of Liquid Top Edge^1.5)))

Coefficient of Discharge given Time of Emptying Hemispherical Tank

Go Coefficient of Discharge = (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*Area of Orifice*(sqrt(2*9.81)))

Coefficient of Discharge given Time of Emptying Circular Horizontal Tank

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

Coefficient of Discharge given Time for Emptying Tank

Go Coefficient of Discharge = (2*Area of Tank*((sqrt(Initial Height of Liquid))-(sqrt(Final Height of Liquid))))/(Total Time Taken*Area of Orifice*sqrt(2*9.81))

Discharge through fully sub-merged orifice

Go Discharge through Orifice = Coefficient of Discharge*Width*(Height of Liquid Bottom Edge-Height of Liquid Top Edge)*(sqrt(2*9.81*Difference in Liquid Level))

Discharge through large rectangular orifice

Go Discharge through Orifice = (2/3)*Coefficient of Discharge*Thickness of Dam*(sqrt(2*9.81))*((Height of Liquid Bottom Edge^1.5)-(Height of Liquid Top Edge^1.5))

Coefficient of discharge for area and velocity

Go Coefficient of Discharge = (Actual Velocity*Actual Area)/(Theoretical Velocity*Theoretical Area)

Discharge in Convergent-Divergent Mouthpiece

Go Discharge through Mouthpiece = Area at Vena Contracta*sqrt(2*9.81*Constant Head)

Discharge in Borda's Mouthpiece Running Full

Go Discharge through Mouthpiece = 0.707*Area*sqrt(2*9.81*Constant Head)

Discharge in Borda's Mouthpiece Running Free

Go Discharge through Mouthpiece = 0.5*Area*sqrt(2*9.81*Constant Head)

Coefficient of discharge

Go Coefficient of Discharge = Actual Discharge/Theoretical Discharge

Coefficient of Discharge given 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 Coefficient of Discharge given Time of Emptying Hemispherical Tank?

Coefficient of Discharge given Time of Emptying Hemispherical Tank calculator uses Coefficient of Discharge = (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*Area of Orifice*(sqrt(2*9.81))) to calculate the Coefficient of Discharge, The Coefficient of Discharge given Time of Emptying Hemispherical Tank is known while considering a hemispherical tank of radius R fitted with an orifice of area 'a' at its bottom. Coefficient of Discharge is denoted by C_d symbol.

How to calculate Coefficient of Discharge given Time of Emptying Hemispherical Tank using this online calculator? To use this online calculator for Coefficient of Discharge 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) & Area of Orifice (a) and hit the calculate button. Here is how the Coefficient of Discharge given Time of Emptying Hemispherical Tank calculation can be explained with given input values -> 0.388329 = (pi*(((4/3)*15*((24^(3/2))-(20.1^(3/2))))-((2/5)*((24^(5/2))-(20.1)^(5/2)))))/(30*9.1*(sqrt(2*9.81))).

FAQ

What is Coefficient of Discharge given Time of Emptying Hemispherical Tank?

The Coefficient of Discharge given Time of Emptying Hemispherical Tank is known while considering a hemispherical tank of radius R fitted with an orifice of area 'a' at its bottom and is represented as C_d = (pi*(((4/3)*R_t*((H_i^(3/2))-(H_f^(3/2))))-((2/5)*((H_i^(5/2))-(H_f)^(5/2)))))/(t_total*a*(sqrt(2*9.81))) or Coefficient of Discharge = (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*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, Total Time Taken is the total time taken by the body to cover that space & 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 Coefficient of Discharge given Time of Emptying Hemispherical Tank?

The Coefficient of Discharge given Time of Emptying Hemispherical Tank is known while considering a hemispherical tank of radius R fitted with an orifice of area 'a' at its bottom is calculated using Coefficient of Discharge = (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*Area of Orifice*(sqrt(2*9.81))). To calculate Coefficient of Discharge given Time of Emptying Hemispherical Tank, you need Hemispherical Tank Radius (R_t), Initial Height of Liquid (H_i), Final Height of Liquid (H_f), Total Time Taken (t_total) & 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, Total Time Taken & 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 Coefficient of Discharge?

In this formula, Coefficient of Discharge uses Hemispherical Tank Radius, Initial Height of Liquid, Final Height of Liquid, Total Time Taken & Area of Orifice. We can use 4 other way(s) to calculate the same, which is/are as follows -

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

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