Head at Entrance of Section given Discharge Flow through Channel Solution

STEP 0: Pre-Calculation Summary
Formula Used
Loss of Head at Exit = 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
ho = hi-(Q/(Cd*Ai*Af*(sqrt(2*[g]/(Ai^2-Af^2)))))^2
This formula uses 1 Constants, 1 Functions, 6 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
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
Loss of Head at Exit - (Measured in Meter) - The Loss of Head at Exit of a pipe is due to the velocity of liquid dissipated in the form of a free jet.
Loss of Head at Entrance - (Measured in Meter) - 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.
Discharge of Channel - (Measured in Cubic Meter per Second) - Discharge of Channel is the rate of flow of a liquid.
Coefficient of Discharge - Coefficient of Discharge is ratio of Actual discharge to theoretical discharge.
Cross Section Area 1 - (Measured in Square Meter) - Cross Section Area 1 is the area of cross section at the inlet of the structure (venturimeter or pipe).
Cross Section Area 2 - (Measured in Square Meter) - Cross Section Area 2 is defined as the area of cross-section at the throat (venturimeter) of the structure.
STEP 1: Convert Input(s) to Base Unit
Loss of Head at Entrance: 20 Meter --> 20 Meter No Conversion Required
Discharge of Channel: 14 Cubic Meter per Second --> 14 Cubic Meter per Second No Conversion Required
Coefficient of Discharge: 0.66 --> No Conversion Required
Cross Section Area 1: 7.1 Square Meter --> 7.1 Square Meter No Conversion Required
Cross Section Area 2: 1.8 Square Meter --> 1.8 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ho = hi-(Q/(Cd*Ai*Af*(sqrt(2*[g]/(Ai^2-Af^2)))))^2 --> 20-(14/(0.66*7.1*1.8*(sqrt(2*[g]/(7.1^2-1.8^2)))))^2
Evaluating ... ...
ho = 13.3744536326731
STEP 3: Convert Result to Output's Unit
13.3744536326731 Meter --> No Conversion Required
FINAL ANSWER
13.3744536326731 13.37445 Meter <-- Loss of Head at Exit
(Calculation completed in 00.004 seconds)

Credits

Created by Rithik Agrawal
National Institute of Technology Karnataka (NITK), Surathkal
Rithik Agrawal has created this Calculator and 1300+ more calculators!
Verified by Ishita Goyal
Meerut Institute of Engineering and Technology (MIET), Meerut
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Coefficient of Discharge through Flume given Discharge Flow through Rectangular Channel
Go Coefficient of Discharge = (Discharge of Channel/(Cross Section Area 1*Cross Section Area 2)*(sqrt(((Cross Section Area 1^2)-(Cross Section Area 2^2))/(2*[g]*(Loss of Head at Entrance-Loss of Head at Exit)))))
Coefficient of Discharge through Flume given Discharge Flow through Channel
Go Coefficient of Discharge = (Discharge of Channel/(Cross Section Area 1*Cross Section Area 2)*(sqrt(((Cross Section Area 1^2)-(Cross Section Area 2^2))/(2*[g]*(Loss of Head at Entrance-Loss of Head at Exit)))))
Discharge Flow through Rectangular Channel
Go Discharge of Channel = (Coefficient of Discharge*Cross Section Area 1*Cross Section Area 2)*(sqrt(2*[g]*(Loss of Head at Entrance-Loss of Head at Exit)/((Cross Section Area 1^2)-(Cross Section Area 2^2))))
Discharge Flow through Channel
Go Discharge of Channel = (Coefficient of Discharge*Cross Section Area 1*Cross Section Area 2)*(sqrt(2*[g]*(Loss of Head at Entrance-Loss of Head at Exit)/((Cross Section Area 1^2)-(Cross Section Area 2^2))))
Head at Entrance of Section given Discharge Flow through Channel
Go Loss of Head at Exit = 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
Head at Entrance given Discharge through Channel
Go 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
Depth of Flow given Discharge through Critical Depth Flume
Go Depth of Flow = (Discharge of Channel/(Width of Throat*Coefficient of Discharge))^(2/3)
Discharge Coefficient given Discharge through Critical Depth Flume
Go Coefficient of Discharge = Discharge of Channel/(Width of Throat*(Depth of Flow^1.5))
Width of Throat given Discharge through Critical Depth Flume
Go Width of Throat = Discharge of Channel/(Coefficient of Discharge*(Depth of Flow^1.5))
Discharge through Critical Depth Flume
Go Discharge of Channel = Coefficient of Discharge*Width of Throat*(Depth of Flow^1.5)

Head at Entrance of Section given Discharge Flow through Channel Formula

Loss of Head at Exit = 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
ho = hi-(Q/(Cd*Ai*Af*(sqrt(2*[g]/(Ai^2-Af^2)))))^2

What is Rate of Flow?

In physics and engineering, in particular fluid dynamics, the volumetric flow rate is the volume of fluid which passes per unit time; usually it is represented by the symbol Q. The SI unit is cubic metres per second. Another unit used is standard cubic centimetres per minute. In hydrometry, it is known as discharge.

How to Calculate Head at Entrance of Section given Discharge Flow through Channel?

Head at Entrance of Section given Discharge Flow through Channel calculator uses Loss of Head at Exit = 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 to calculate the Loss of Head at Exit, The Head at Entrance of Section given Discharge flow through Channel is defined as head at section in length of pipe. Loss of Head at Exit is denoted by ho symbol.

How to calculate Head at Entrance of Section given Discharge Flow through Channel using this online calculator? To use this online calculator for Head at Entrance of Section given Discharge Flow through Channel, enter Loss of Head at Entrance (hi), Discharge of Channel (Q), Coefficient of Discharge (Cd), Cross Section Area 1 (Ai) & Cross Section Area 2 (Af) and hit the calculate button. Here is how the Head at Entrance of Section given Discharge Flow through Channel calculation can be explained with given input values -> 13.37445 = 20-(14/(0.66*7.1*1.8*(sqrt(2*[g]/(7.1^2-1.8^2)))))^2.

FAQ

What is Head at Entrance of Section given Discharge Flow through Channel?
The Head at Entrance of Section given Discharge flow through Channel is defined as head at section in length of pipe and is represented as ho = hi-(Q/(Cd*Ai*Af*(sqrt(2*[g]/(Ai^2-Af^2)))))^2 or Loss of Head at Exit = 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. 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, Discharge of Channel is the rate of flow of a liquid, Coefficient of Discharge is ratio of Actual discharge to theoretical discharge, Cross Section Area 1 is the area of cross section at the inlet of the structure (venturimeter or pipe) & Cross Section Area 2 is defined as the area of cross-section at the throat (venturimeter) of the structure.
How to calculate Head at Entrance of Section given Discharge Flow through Channel?
The Head at Entrance of Section given Discharge flow through Channel is defined as head at section in length of pipe is calculated using Loss of Head at Exit = 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. To calculate Head at Entrance of Section given Discharge Flow through Channel, you need Loss of Head at Entrance (hi), Discharge of Channel (Q), Coefficient of Discharge (Cd), Cross Section Area 1 (Ai) & Cross Section Area 2 (Af). With our tool, you need to enter the respective value for Loss of Head at Entrance, Discharge of Channel, Coefficient of Discharge, Cross Section Area 1 & Cross Section Area 2 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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