Rate of Flow given Pressure Gradient Calculator

✖The Mean Velocity refers to the average rate at which an object or fluid moves over a given time interval.ⓘ Mean Velocity [V_mean]			+10% -10%
✖The Height of Channel refers to the flow depth or water level within the channel. Height refers to the flow depth or water level within the channel.ⓘ Height of Channel [h]			+10% -10%
✖The Pressure Gradient refers to the rate of change of pressure in a particular direction indicating how quickly the pressure increases or decreases around a specific location.ⓘ Pressure Gradient [dp\|dr]			+10% -10%
✖The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.ⓘ Dynamic Viscosity [μ]			+10% -10%

✖The Discharge in Pipe refers to the volume of fluid (such as water) that passes through the pipe per unit of time.ⓘ Rate of Flow given Pressure Gradient [Q]

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Rate of Flow given Pressure Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Discharge in Pipe = 0.5*Mean Velocity*Height of Channel-(Pressure Gradient*(Height of Channel^3)/(12*Dynamic Viscosity))
Q = 0.5*V_mean*h-(dp|dr*(h^3)/(12*μ))
This formula uses 5 Variables

Variables Used

Discharge in Pipe - (Measured in Cubic Meter per Second) - The Discharge in Pipe refers to the volume of fluid (such as water) that passes through the pipe per unit of time.
Mean Velocity - (Measured in Meter per Second) - The Mean Velocity refers to the average rate at which an object or fluid moves over a given time interval.
Height of Channel - (Measured in Meter) - The Height of Channel refers to the flow depth or water level within the channel. Height refers to the flow depth or water level within the channel.
Pressure Gradient - (Measured in Newton per Cubic Meter) - The Pressure Gradient refers to the rate of change of pressure in a particular direction indicating how quickly the pressure increases or decreases around a specific location.
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.

STEP 1: Convert Input(s) to Base Unit

Mean Velocity: 10 Meter per Second --> 10 Meter per Second No Conversion Required
Height of Channel: 1.81 Meter --> 1.81 Meter No Conversion Required
Pressure Gradient: 17 Newton per Cubic Meter --> 17 Newton per Cubic Meter No Conversion Required
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = 0.5*V_mean*h-(dp|dr*(h^3)/(12*μ)) --> 0.5*10*1.81-(17*(1.81^3)/(12*1.02))

Evaluating ... ...

Q = 0.814248611111111

STEP 3: Convert Result to Output's Unit

0.814248611111111 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

0.814248611111111 ≈ 0.814249 Cubic Meter per Second <-- Discharge in Pipe

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Dynamic Viscosity given Pressure Gradient

LaTeX Go Dynamic Viscosity = Pressure Gradient*(Height of Channel^3)/(12*(0.5*Mean Velocity*Height of Channel-Discharge in Pipe))

Rate of Flow given Pressure Gradient

LaTeX Go Discharge in Pipe = 0.5*Mean Velocity*Height of Channel-(Pressure Gradient*(Height of Channel^3)/(12*Dynamic Viscosity))

Pressure Gradient

LaTeX Go Pressure Gradient = (12*Dynamic Viscosity/(Height of Channel^3))*(0.5*Mean Velocity*Height of Channel-Discharge in Pipe)

Rate of Flow given Pressure Gradient Formula

LaTeX Go

Discharge in Pipe = 0.5*Mean Velocity*Height of Channel-(Pressure Gradient*(Height of Channel^3)/(12*Dynamic Viscosity))
Q = 0.5*V_mean*h-(dp|dr*(h^3)/(12*μ))

What is Pressure Gradient?

Pressure gradient is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pascals per metre.

What is Dynamic Viscosity?

The dynamic viscosity η (η = "eta") is a measure of the viscosity of a fluid (fluid: liquid, flowing substance). The higher the viscosity, the thicker (less liquid) the fluid; the lower the viscosity, the thinner (more liquid) it is.

How to Calculate Rate of Flow given Pressure Gradient?

Rate of Flow given Pressure Gradient calculator uses Discharge in Pipe = 0.5*Mean Velocity*Height of Channel-(Pressure Gradient*(Height of Channel^3)/(12*Dynamic Viscosity)) to calculate the Discharge in Pipe, The Rate of Flow given Pressure Gradient formula is defined as the flow rate that is directly proportional to the pressure difference and the fourth power of the pipe radius, and inversely proportional to the fluid’s viscosity and the pipe length. Discharge in Pipe is denoted by Q symbol.

How to calculate Rate of Flow given Pressure Gradient using this online calculator? To use this online calculator for Rate of Flow given Pressure Gradient, enter Mean Velocity (V_mean), Height of Channel (h), Pressure Gradient (dp|dr) & Dynamic Viscosity (μ) and hit the calculate button. Here is how the Rate of Flow given Pressure Gradient calculation can be explained with given input values -> 0.814249 = 0.5*10*1.81-(17*(1.81^3)/(12*1.02)).

FAQ

What is Rate of Flow given Pressure Gradient?

The Rate of Flow given Pressure Gradient formula is defined as the flow rate that is directly proportional to the pressure difference and the fourth power of the pipe radius, and inversely proportional to the fluid’s viscosity and the pipe length and is represented as Q = 0.5*V_mean*h-(dp|dr*(h^3)/(12*μ)) or Discharge in Pipe = 0.5*Mean Velocity*Height of Channel-(Pressure Gradient*(Height of Channel^3)/(12*Dynamic Viscosity)). The Mean Velocity refers to the average rate at which an object or fluid moves over a given time interval, The Height of Channel refers to the flow depth or water level within the channel. Height refers to the flow depth or water level within the channel, The Pressure Gradient refers to the rate of change of pressure in a particular direction indicating how quickly the pressure increases or decreases around a specific location & The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.

How to calculate Rate of Flow given Pressure Gradient?

The Rate of Flow given Pressure Gradient formula is defined as the flow rate that is directly proportional to the pressure difference and the fourth power of the pipe radius, and inversely proportional to the fluid’s viscosity and the pipe length is calculated using Discharge in Pipe = 0.5*Mean Velocity*Height of Channel-(Pressure Gradient*(Height of Channel^3)/(12*Dynamic Viscosity)). To calculate Rate of Flow given Pressure Gradient, you need Mean Velocity (V_mean), Height of Channel (h), Pressure Gradient (dp|dr) & Dynamic Viscosity (μ). With our tool, you need to enter the respective value for Mean Velocity, Height of Channel, Pressure Gradient & Dynamic Viscosity 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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