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Head at Entrance given Discharge through Channel Formula

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The Loss of Head at Entrance of a pipe is the loss that occurs when a liquid flows from a large tank into a pipe. Check FAQs

h i = {(\frac{Q}{C d \cdot A i \cdot A f \cdot (\sqrt{2 \cdot \frac{[g]}{{A i}^{2} - {A f}^{2}}})})}^{2} + h o

h_i - Loss of Head at Entrance?Q - Discharge of Channel?C_d - Coefficient of Discharge?A_i - Cross Section Area 1?A_f - Cross Section Area 2?h_o - Loss of Head at Exit?[g] - Gravitational acceleration on Earth?

Head at Entrance given Discharge through Channel Example

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Here is how the Head at Entrance given Discharge through Channel equation looks like with Values.

Here is how the Head at Entrance given Discharge through Channel equation looks like with Units.

Here is how the Head at Entrance given Discharge through Channel equation looks like.

21.7255 = {(\frac{14}{0.66 \cdot 7.1 \cdot 1.8 \cdot (\sqrt{2 \cdot \frac{9.8066}{{7.1}^{2} - {1.8}^{2}}})})}^{2} + 15.1

21.7255m = {(\frac{14m³/s}{0.66 \cdot 7.1m² \cdot 1.8m² \cdot (\sqrt{2 \cdot \frac{9.8066m/s²}{{7.1m²}^{2} - {1.8m²}^{2}}})})}^{2} + 15.1m

21.7255 = {(\frac{14}{0.66 \cdot 7.1 \cdot 1.8 \cdot (\sqrt{2 \cdot \frac{9.8066}{{7.1}^{2} - {1.8}^{2}}})})}^{2} + 15.1

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Head at Entrance given Discharge through Channel Solution

Follow our step by step solution on how to calculate Head at Entrance given Discharge through Channel?

FIRST Step Consider the formula

h i = {(\frac{Q}{C d \cdot A i \cdot A f \cdot (\sqrt{2 \cdot \frac{[g]}{{A i}^{2} - {A f}^{2}}})})}^{2} + h o

Next Step Substitute values of Variables

∴

h i = {(\frac{14m³/s}{0.66 \cdot 7.1m² \cdot 1.8m² \cdot (\sqrt{2 \cdot \frac{[g]}{{7.1m²}^{2} - {1.8m²}^{2}}})})}^{2} + 15.1m

Next Step Substitute values of Constants

∴

h i = {(\frac{14m³/s}{0.66 \cdot 7.1m² \cdot 1.8m² \cdot (\sqrt{2 \cdot \frac{9.8066m/s²}{{7.1m²}^{2} - {1.8m²}^{2}}})})}^{2} + 15.1m

Next Step Prepare to Evaluate

∴

h i = {(\frac{14}{0.66 \cdot 7.1 \cdot 1.8 \cdot (\sqrt{2 \cdot \frac{9.8066}{{7.1}^{2} - {1.8}^{2}}})})}^{2} + 15.1

Next Step Evaluate

∴

h i = 21.7255463673269m

LAST Step Rounding Answer

∴

h i = 21.7255m

Head at Entrance given Discharge through Channel Formula Elements

Variables

Constants

Functions

Loss of Head at Entrance

The Loss of Head at Entrance of a pipe is the loss that occurs when a liquid flows from a large tank into a pipe.

Symbol: h_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Loss of Head at Entrance

Discharge of Channel

Discharge of Channel is the rate of flow of a liquid.

Symbol: Q

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge of Channel

Coefficient of Discharge

The Coefficient of Discharge is ratio of actual discharge to theoretical discharge.

Symbol: C_d

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.2.

Formulas to find Coefficient of Discharge

Cross Section Area 1

Cross Section Area 1 is the area of cross section at the inlet of the structure (venturimeter or pipe).

Symbol: A_i

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Section Area 1

Cross Section Area 2

Cross Section Area 2 is defined as the area of cross-section at the throat (venturimeter) of the structure.

Symbol: A_f

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Section Area 2

Loss of Head at Exit

The Loss of Head at Exit of a pipe is due to the velocity of liquid dissipated in the form of a free jet.

Symbol: h_o

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Loss of Head at Exit

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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 in Metering Flumes category

Go Discharge Flow through Channel

Q = (C d \cdot A i \cdot A f) \cdot (\sqrt{2 \cdot [g] \cdot \frac{h i - h o}{({A i}^{2}) - ({A f}^{2})}})

Go Coefficient of Discharge through Flume given Discharge Flow through Channel

C d = (\frac{Q}{A i \cdot A f} \cdot (\sqrt{\frac{({A i}^{2}) - ({A f}^{2})}{2 \cdot [g] \cdot (h i - h o)}}))

Go Head at Entrance of Section given Discharge Flow through Channel

h o = h i - {(\frac{Q}{C d \cdot A i \cdot A f \cdot (\sqrt{2 \cdot \frac{[g]}{{A i}^{2} - {A f}^{2}}})})}^{2}

Go Discharge Flow through Rectangular Channel

Q = (C d \cdot A i \cdot A f) \cdot (\sqrt{2 \cdot [g] \cdot \frac{h i - h o}{({A i}^{2}) - ({A f}^{2})}})

How to Evaluate Head at Entrance given Discharge through Channel?

Head at Entrance given Discharge through Channel evaluator uses Loss of Head at Entrance = (Discharge of Channel/(Coefficient of Discharge*Cross Section Area 1*Cross Section Area 2*(sqrt(2*[g]/(Cross Section Area 1^2-Cross Section Area 2^2)))))^2+Loss of Head at Exit to evaluate the Loss of Head at Entrance, The Head at Entrance given Discharge through Channel is defined as head at section in length of pipe. Loss of Head at Entrance is denoted by h_i symbol.

How to evaluate Head at Entrance given Discharge through Channel using this online evaluator? To use this online evaluator for Head at Entrance given Discharge through Channel, enter Discharge of Channel (Q), Coefficient of Discharge (C_d), Cross Section Area 1 (A_i), Cross Section Area 2 (A_f) & Loss of Head at Exit (h_o) and hit the calculate button.

FAQs on Head at Entrance given Discharge through Channel

What is the formula to find Head at Entrance given Discharge through Channel?

The formula of Head at Entrance given Discharge through Channel is expressed as Loss of Head at Entrance = (Discharge of Channel/(Coefficient of Discharge*Cross Section Area 1*Cross Section Area 2*(sqrt(2*[g]/(Cross Section Area 1^2-Cross Section Area 2^2)))))^2+Loss of Head at Exit. Here is an example- 21.72555 = (14/(0.66*7.1*1.8*(sqrt(2*[g]/(7.1^2-1.8^2)))))^2+15.1.

How to calculate Head at Entrance given Discharge through Channel?

With Discharge of Channel (Q), Coefficient of Discharge (C_d), Cross Section Area 1 (A_i), Cross Section Area 2 (A_f) & Loss of Head at Exit (h_o) we can find Head at Entrance given Discharge through Channel using the formula - Loss of Head at Entrance = (Discharge of Channel/(Coefficient of Discharge*Cross Section Area 1*Cross Section Area 2*(sqrt(2*[g]/(Cross Section Area 1^2-Cross Section Area 2^2)))))^2+Loss of Head at Exit. This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

Can the Head at Entrance given Discharge through Channel be negative?

No, the Head at Entrance given Discharge through Channel, measured in Length cannot be negative.

Which unit is used to measure Head at Entrance given Discharge through Channel?

Head at Entrance given Discharge through Channel is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Head at Entrance given Discharge through Channel can be measured.

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Head at Entrance given Discharge through Channel Formula

Head at Entrance given Discharge through Channel Example

Head at Entrance given Discharge through Channel Solution

Head at Entrance given Discharge through Channel Formula Elements

Other formulas in Metering Flumes category

How to Evaluate Head at Entrance given Discharge through Channel?

FAQs on Head at Entrance given Discharge through Channel

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