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Coefficient of Discharge given Time of Emptying Hemispherical Tank Formula

GoCoefficient of discharge Formula

GoCoefficient of discharge for area and velocity Formula

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The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge. Check FAQs

C d = \frac{π \cdot (((\frac{4}{3}) \cdot R t \cdot (({H i}^{\frac{3}{2}}) - ({H f}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot (({H i}^{\frac{5}{2}}) - {(H f)}^{\frac{5}{2}})))}{t total \cdot a \cdot (\sqrt{2 \cdot 9.81})}

C_d - Coefficient of Discharge?R_t - Hemispherical Tank Radius?H_i - Initial Height of Liquid?H_f - Final Height of Liquid?t_total - Total Time Taken?a - Area of Orifice?π - Archimedes' constant?

Coefficient of Discharge given Time of Emptying Hemispherical Tank Example

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Here is how the Coefficient of Discharge given Time of Emptying Hemispherical Tank equation looks like with Values.

Here is how the Coefficient of Discharge given Time of Emptying Hemispherical Tank equation looks like with Units.

Here is how the Coefficient of Discharge given Time of Emptying Hemispherical Tank equation looks like.

0.3768 = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15 \cdot ((24^{\frac{3}{2}}) - ({20.1}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot ((24^{\frac{5}{2}}) - {(20.1)}^{\frac{5}{2}})))}{30 \cdot 9.1 \cdot (\sqrt{2 \cdot 9.81})}

0.3768 = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15m \cdot (({24m}^{\frac{3}{2}}) - ({20.1m}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot (({24m}^{\frac{5}{2}}) - {(20.1m)}^{\frac{5}{2}})))}{30s \cdot 9.1m² \cdot (\sqrt{2 \cdot 9.81})}

0.3768 = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15 \cdot ((24^{\frac{3}{2}}) - ({20.1}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot ((24^{\frac{5}{2}}) - {(20.1)}^{\frac{5}{2}})))}{30 \cdot 9.1 \cdot (\sqrt{2 \cdot 9.81})}

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Coefficient of Discharge given Time of Emptying Hemispherical Tank Solution

Follow our step by step solution on how to calculate Coefficient of Discharge given Time of Emptying Hemispherical Tank?

FIRST Step Consider the formula

C d = \frac{π \cdot (((\frac{4}{3}) \cdot R t \cdot (({H i}^{\frac{3}{2}}) - ({H f}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot (({H i}^{\frac{5}{2}}) - {(H f)}^{\frac{5}{2}})))}{t total \cdot a \cdot (\sqrt{2 \cdot 9.81})}

Next Step Substitute values of Variables

∴

C d = \frac{π \cdot (((\frac{4}{3}) \cdot 15m \cdot (({24m}^{\frac{3}{2}}) - ({20.1m}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot (({24m}^{\frac{5}{2}}) - {(20.1m)}^{\frac{5}{2}})))}{30s \cdot 9.1m² \cdot (\sqrt{2 \cdot 9.81})}

Next Step Substitute values of Constants

∴

C d = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15m \cdot (({24m}^{\frac{3}{2}}) - ({20.1m}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot (({24m}^{\frac{5}{2}}) - {(20.1m)}^{\frac{5}{2}})))}{30s \cdot 9.1m² \cdot (\sqrt{2 \cdot 9.81})}

Next Step Prepare to Evaluate

∴

C d = \frac{3.1416 \cdot (((\frac{4}{3}) \cdot 15 \cdot ((24^{\frac{3}{2}}) - ({20.1}^{\frac{3}{2}}))) - ((\frac{2}{5}) \cdot ((24^{\frac{5}{2}}) - {(20.1)}^{\frac{5}{2}})))}{30 \cdot 9.1 \cdot (\sqrt{2 \cdot 9.81})}

Next Step Evaluate

∴

C d = 0.376753780994054

LAST Step Rounding Answer

∴

C d = 0.3768

Coefficient of Discharge given Time of Emptying Hemispherical Tank Formula Elements

Variables

Constants

Functions

Coefficient of Discharge

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

Symbol: C_d

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Coefficient of Discharge

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.

Symbol: R_t

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Hemispherical Tank Radius

Initial Height of Liquid

The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom.

Symbol: H_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Initial Height of Liquid

Final Height of Liquid

The Final height of liquid is a variable from the tank emptying through an orifice at its bottom.

Symbol: H_f

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Final Height of Liquid

Total Time Taken

Total Time Taken is the total time taken by the body to cover that space.

Symbol: t_total

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Total Time Taken

Area of Orifice

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).

Symbol: a

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Orifice

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Coefficient of Discharge

Go Coefficient of discharge

C d = \frac{Q a}{Q th}

Go Coefficient of discharge for area and velocity

C d = \frac{v a \cdot A a}{V th \cdot A t}

Go Coefficient of Discharge given Time for Emptying Tank

C d = \frac{2 \cdot A T \cdot ((\sqrt{H i}) - (\sqrt{H f}))}{t total \cdot a \cdot \sqrt{2 \cdot 9.81}}

Go Coefficient of Discharge given Time of Emptying Circular Horizontal Tank

C d = \frac{4 \cdot L \cdot (({((2 \cdot r 1) - H f)}^{\frac{3}{2}}) - {((2 \cdot r 1) - H i)}^{\frac{3}{2}})}{3 \cdot t total \cdot a \cdot (\sqrt{2 \cdot 9.81})}

Other formulas in Flow Rate category

Go Discharge through large rectangular orifice

Q O = (\frac{2}{3}) \cdot C d \cdot b \cdot (\sqrt{2 \cdot 9.81}) \cdot (({H b}^{1.5}) - ({H top}^{1.5}))

Go Discharge through fully sub-merged orifice

Q O = C d \cdot w \cdot (H b - H top) \cdot (\sqrt{2 \cdot 9.81 \cdot H L})

Go Discharge through partially sub-merged orifice

Q O = (C d \cdot w \cdot (H b - H L) \cdot (\sqrt{2 \cdot 9.81 \cdot H L})) + ((\frac{2}{3}) \cdot C d \cdot b \cdot (\sqrt{2 \cdot 9.81}) \cdot (({H L}^{1.5}) - ({H top}^{1.5})))

Go Discharge in Convergent-Divergent Mouthpiece

Q M = a c \cdot \sqrt{2 \cdot 9.81 \cdot H c}

How to Evaluate Coefficient of Discharge given Time of Emptying Hemispherical Tank?

Coefficient of Discharge given Time of Emptying Hemispherical Tank evaluator 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 evaluate 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 evaluate Coefficient of Discharge given Time of Emptying Hemispherical Tank using this online evaluator? To use this online evaluator 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.

FAQs on Coefficient of Discharge given Time of Emptying Hemispherical Tank

What is the formula to find Coefficient of Discharge given Time of Emptying Hemispherical Tank?

The formula of Coefficient of Discharge given Time of Emptying Hemispherical Tank is expressed as 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))). Here is an example- 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))).

How to calculate Coefficient of Discharge given Time of Emptying Hemispherical Tank?

With 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) we can find Coefficient of Discharge given Time of Emptying Hemispherical Tank using the formula - 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))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Coefficient of Discharge?

Here are the different ways to Calculate Coefficient of Discharge-

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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Coefficient of Discharge given Time of Emptying Hemispherical Tank Formula

​GoCoefficient of discharge Formula

​GoCoefficient of discharge for area and velocity Formula

Coefficient of Discharge given Time of Emptying Hemispherical Tank Example

Coefficient of Discharge given Time of Emptying Hemispherical Tank Solution

Coefficient of Discharge given Time of Emptying Hemispherical Tank Formula Elements

Other Formulas to find Coefficient of Discharge

Other formulas in Flow Rate category

How to Evaluate Coefficient of Discharge given Time of Emptying Hemispherical Tank?

FAQs on Coefficient of Discharge given Time of Emptying Hemispherical Tank

Variable Name

GoCoefficient of discharge Formula

GoCoefficient of discharge for area and velocity Formula