Discharge through partially sub-merged orifice Calculator

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Orifices and Mouthpieces

Draft Tube

Properties of Surfaces and Solids

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✖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%
✖Width is the measurement or extent of something from side to side.ⓘ Width [w]			+10% -10%
✖Height of liquid bottom edge is a variable in discharge through the large rectangular orifice.ⓘ Height of Liquid Bottom Edge [H_bottom]			+10% -10%
✖The Difference in liquid level is a variable in discharge through the fully submerged orifice.ⓘ Difference in Liquid Level [H_L]			+10% -10%
✖Thickness of Dam is the measurement or extent of dam from side to side.ⓘ Thickness of Dam [b]			+10% -10%
✖Height of liquid top edge is a variable in discharge through the large rectangular orifice.ⓘ Height of Liquid Top Edge [H_top]			+10% -10%

✖The Discharge through orifice is an opening, of any size or shape, in a pipe or at the bottom or side wall of a container (water tank, reservoir, etc.), through which fluid is discharged.ⓘ Discharge through partially sub-merged orifice [Q_O]

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Formula

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Discharge through partially sub-merged orifice

Formula

`"Q"_{"O"} = ("C"_{"d"}*"w"*("H"_{"bottom"}-"H"_{"L"})*(sqrt(2*9.81*"H"_{"L"})))+((2/3)*"C"_{"d"}*"b"*(sqrt(2*9.81))*(("H"_{"L"}^1.5)-("H"_{"top"}^1.5)))`

Example

`"100.2577m³/s"=("0.87"*"3.5m"*("20m"-"9.5m")*(sqrt(2*9.81*"9.5m")))+((2/3)*"0.87"*"2.2m"*(sqrt(2*9.81))*((("9.5m")^1.5)-(("19.9m")^1.5)))`

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Discharge through partially sub-merged orifice Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
Q_O = (C_d*w*(H_bottom-H_L)*(sqrt(2*9.81*H_L)))+((2/3)*C_d*b*(sqrt(2*9.81))*((H_L^1.5)-(H_top^1.5)))
This formula uses 1 Functions, 7 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

Discharge through Orifice - (Measured in Cubic Meter per Second) - The Discharge through orifice is an opening, of any size or shape, in a pipe or at the bottom or side wall of a container (water tank, reservoir, etc.), through which fluid is discharged.
Coefficient of Discharge - The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge.
Width - (Measured in Meter) - Width is the measurement or extent of something from side to side.
Height of Liquid Bottom Edge - (Measured in Meter) - Height of liquid bottom edge is a variable in discharge through the large rectangular orifice.
Difference in Liquid Level - (Measured in Meter) - The Difference in liquid level is a variable in discharge through the fully submerged orifice.
Thickness of Dam - (Measured in Meter) - Thickness of Dam is the measurement or extent of dam from side to side.
Height of Liquid Top Edge - (Measured in Meter) - Height of liquid top edge is a variable in discharge through the large rectangular orifice.

STEP 1: Convert Input(s) to Base Unit

Coefficient of Discharge: 0.87 --> No Conversion Required
Width: 3.5 Meter --> 3.5 Meter No Conversion Required
Height of Liquid Bottom Edge: 20 Meter --> 20 Meter No Conversion Required
Difference in Liquid Level: 9.5 Meter --> 9.5 Meter No Conversion Required
Thickness of Dam: 2.2 Meter --> 2.2 Meter No Conversion Required
Height of Liquid Top Edge: 19.9 Meter --> 19.9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_O = (C_d*w*(H_bottom-H_L)*(sqrt(2*9.81*H_L)))+((2/3)*C_d*b*(sqrt(2*9.81))*((H_L^1.5)-(H_top^1.5))) --> (0.87*3.5*(20-9.5)*(sqrt(2*9.81*9.5)))+((2/3)*0.87*2.2*(sqrt(2*9.81))*((9.5^1.5)-(19.9^1.5)))

Evaluating ... ...

Q_O = 100.257709544982

STEP 3: Convert Result to Output's Unit

100.257709544982 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

100.257709544982 ≈ 100.2577 Cubic Meter per Second <-- Discharge through Orifice

(Calculation completed in 00.004 seconds)

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PSG College of Technology (PSGCT), Coimbatore

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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

Discharge through partially sub-merged orifice Formula

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 Discharge through partially sub-merged orifice?

Discharge through partially sub-merged orifice calculator uses 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))) to calculate the Discharge through Orifice, The Discharge through partially sub-merged orifice formula is the one that has its outlet side partially submerged under the liquid. It is also known as partially drowned orifice. Discharge through Orifice is denoted by Q_O symbol.

How to calculate Discharge through partially sub-merged orifice using this online calculator? To use this online calculator for Discharge through partially sub-merged orifice, enter Coefficient of Discharge (C_d), Width (w), Height of Liquid Bottom Edge (H_bottom), Difference in Liquid Level (H_L), Thickness of Dam (b) & Height of Liquid Top Edge (H_top) and hit the calculate button. Here is how the Discharge through partially sub-merged orifice calculation can be explained with given input values -> 100.2577 = (0.87*3.5*(20-9.5)*(sqrt(2*9.81*9.5)))+((2/3)*0.87*2.2*(sqrt(2*9.81))*((9.5^1.5)-(19.9^1.5))).

FAQ

What is Discharge through partially sub-merged orifice?

The Discharge through partially sub-merged orifice formula is the one that has its outlet side partially submerged under the liquid. It is also known as partially drowned orifice and is represented as Q_O = (C_d*w*(H_bottom-H_L)*(sqrt(2*9.81*H_L)))+((2/3)*C_d*b*(sqrt(2*9.81))*((H_L^1.5)-(H_top^1.5))) or 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))). The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge, Width is the measurement or extent of something from side to side, Height of liquid bottom edge is a variable in discharge through the large rectangular orifice, The Difference in liquid level is a variable in discharge through the fully submerged orifice, Thickness of Dam is the measurement or extent of dam from side to side & Height of liquid top edge is a variable in discharge through the large rectangular orifice.

How to calculate Discharge through partially sub-merged orifice?

The Discharge through partially sub-merged orifice formula is the one that has its outlet side partially submerged under the liquid. It is also known as partially drowned orifice is calculated using 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))). To calculate Discharge through partially sub-merged orifice, you need Coefficient of Discharge (C_d), Width (w), Height of Liquid Bottom Edge (H_bottom), Difference in Liquid Level (H_L), Thickness of Dam (b) & Height of Liquid Top Edge (H_top). With our tool, you need to enter the respective value for Coefficient of Discharge, Width, Height of Liquid Bottom Edge, Difference in Liquid Level, Thickness of Dam & Height of Liquid Top Edge 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 Discharge through Orifice?

In this formula, Discharge through Orifice uses Coefficient of Discharge, Width, Height of Liquid Bottom Edge, Difference in Liquid Level, Thickness of Dam & Height of Liquid Top Edge. We can use 2 other way(s) to calculate the same, which is/are as follows -

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))
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))

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