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)))
Cd = (pi*(((4/3)*Rt*((Hi^(3/2))-(Hf^(3/2))))-((2/5)*((Hi^(5/2))-(Hf)^(5/2)))))/(ttotal*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
Cd = (pi*(((4/3)*Rt*((Hi^(3/2))-(Hf^(3/2))))-((2/5)*((Hi^(5/2))-(Hf)^(5/2)))))/(ttotal*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 ... ...
Cd = 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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Flow Rate Calculators

Coefficient of Discharge given Time of Emptying Hemispherical Tank
​ LaTeX ​ 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 for Emptying Tank
​ LaTeX ​ 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))
Coefficient of discharge for area and velocity
​ LaTeX ​ Go Coefficient of Discharge = (Actual Velocity*Actual Area)/(Theoretical Velocity*Theoretical Area)
Coefficient of discharge
​ LaTeX ​ Go Coefficient of Discharge = Actual Discharge/Theoretical Discharge

Coefficient of Discharge given Time of Emptying Hemispherical Tank Formula

​LaTeX ​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)))
Cd = (pi*(((4/3)*Rt*((Hi^(3/2))-(Hf^(3/2))))-((2/5)*((Hi^(5/2))-(Hf)^(5/2)))))/(ttotal*a*(sqrt(2*9.81)))

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 Cd 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 (Rt), Initial Height of Liquid (Hi), Final Height of Liquid (Hf), Total Time Taken (ttotal) & 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 Cd = (pi*(((4/3)*Rt*((Hi^(3/2))-(Hf^(3/2))))-((2/5)*((Hi^(5/2))-(Hf)^(5/2)))))/(ttotal*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 (Rt), Initial Height of Liquid (Hi), Final Height of Liquid (Hf), Total Time Taken (ttotal) & 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 3 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))
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