Coefficient of Discharge given Time for Emptying Tank Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
Cd = (2*AT*((sqrt(Hi))-(sqrt(Hf))))/(ttotal*a*sqrt(2*9.81))
This formula uses 1 Functions, 6 Variables
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.
Area of Tank - (Measured in Square Meter) - The Area of tank is a variable from the concept of emptying the tank through orifice.
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
Area of Tank: 1144 Square Meter --> 1144 Square 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 = (2*AT*((sqrt(Hi))-(sqrt(Hf))))/(ttotal*a*sqrt(2*9.81)) --> (2*1144*((sqrt(24))-(sqrt(20.1))))/(30*9.1*sqrt(2*9.81))
Evaluating ... ...
Cd = 0.786502312252424
STEP 3: Convert Result to Output's Unit
0.786502312252424 --> No Conversion Required
FINAL ANSWER
0.786502312252424 0.786502 <-- Coefficient of Discharge
(Calculation completed in 00.019 seconds)

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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 for Emptying Tank Formula

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))
Cd = (2*AT*((sqrt(Hi))-(sqrt(Hf))))/(ttotal*a*sqrt(2*9.81))

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.

What is an orifice?

The orifice is defined as the small opening on the side or bottom of a tank through which any kind of fluid is flowing. The opening can be circular, triangular, or rectangular in cross-section and they are named on the basis of shape accordingly.

How to Calculate Coefficient of Discharge given Time for Emptying Tank?

Coefficient of Discharge given Time for Emptying Tank calculator uses 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)) to calculate the Coefficient of Discharge, The Coefficient of Discharge given Time for Emptying Tank is known when considering a tank containing some liquid up to a height of H 1. Let 'T' be the time taken for emptying the tank through an orifice at the bottom, 'A' and 'a' be the area of the tank and orifice. Coefficient of Discharge is denoted by Cd symbol.

How to calculate Coefficient of Discharge given Time for Emptying Tank using this online calculator? To use this online calculator for Coefficient of Discharge given Time for Emptying Tank, enter Area of Tank (AT), 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 for Emptying Tank calculation can be explained with given input values -> 0.80763 = (2*1144*((sqrt(24))-(sqrt(20.1))))/(30*9.1*sqrt(2*9.81)).

FAQ

What is Coefficient of Discharge given Time for Emptying Tank?
The Coefficient of Discharge given Time for Emptying Tank is known when considering a tank containing some liquid up to a height of H 1. Let 'T' be the time taken for emptying the tank through an orifice at the bottom, 'A' and 'a' be the area of the tank and orifice and is represented as Cd = (2*AT*((sqrt(Hi))-(sqrt(Hf))))/(ttotal*a*sqrt(2*9.81)) or 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)). The Area of tank is a variable from the concept of emptying the tank through orifice, 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 for Emptying Tank?
The Coefficient of Discharge given Time for Emptying Tank is known when considering a tank containing some liquid up to a height of H 1. Let 'T' be the time taken for emptying the tank through an orifice at the bottom, 'A' and 'a' be the area of the tank and orifice is calculated using 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)). To calculate Coefficient of Discharge given Time for Emptying Tank, you need Area of Tank (AT), 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 Area of Tank, 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 Area of Tank, 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 = (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 = (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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