Area of Orifice given Time of Emptying Hemispherical Tank Calculator

✖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 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 given Time of Emptying Hemispherical Tank [a]

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Area of Orifice given Time of Emptying Hemispherical Tank Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
a = (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*C_d*(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

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

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
Coefficient of Discharge: 0.87 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = (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*C_d*(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*0.87*(sqrt(2*9.81)))

Evaluating ... ...

a = 3.94075793913321

STEP 3: Convert Result to Output's Unit

3.94075793913321 Square Meter --> No Conversion Required

FINAL ANSWER

3.94075793913321 ≈ 3.940758 Square Meter <-- Area of Orifice

(Calculation completed in 00.004 seconds)

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< Geometric Dimensions Calculators

Area of Orifice given Time of Emptying Hemispherical Tank

LaTeX Go 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)))

Area of Tank given Time for Emptying Tank

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

Vertical distance for coefficient of velocity and horizontal distance

LaTeX Go Vertical Distance = (Horizontal Distance^2)/(4*(Coefficient of Velocity^2)*Head of the Liquid)

Area at vena contracta for discharge and constant head

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

Area of Orifice given Time of Emptying Hemispherical Tank Formula

LaTeX Go

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 Area of Orifice given Time of Emptying Hemispherical Tank?

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

FAQ

What is Area of Orifice given Time of Emptying Hemispherical Tank?

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 and is represented as a = (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*C_d*(sqrt(2*9.81))) or 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))). 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 Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge.

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

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 is calculated using 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 calculate Area of Orifice 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) & Coefficient of Discharge (C_d). 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 & Coefficient of Discharge and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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