Rate of Flow given Pressure Gradient Calculator

✖Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.ⓘ Mean Velocity [V_mean]			+10% -10%
✖Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.ⓘ Height [h]			+10% -10%
✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradient [dp\|dr]			+10% -10%
✖The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.ⓘ Dynamic Viscosity [μ_viscosity]			+10% -10%

✖Rate of Flow is the rate at which a liquid or other substance flows through a particular channel, pipe, etc.ⓘ Rate of Flow given Pressure Gradient [q_flow]

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Formula

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Rate of Flow given Pressure Gradient

Formula

`"q"_{"flow"} = 0.5*"V"_{"mean"}*"h"-("dp|dr"*("h"^3)/(12*"μ"_{"viscosity"}))`

Example

`"0.814249m³/s"=0.5*"10m/s"*"1.81m"-("17N/m³"*(("1.81m")^3)/(12*"10.2P"))`

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Rate of Flow given Pressure Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rate of Flow = 0.5*Mean Velocity*Height-(Pressure Gradient*(Height^3)/(12*Dynamic Viscosity))
q_flow = 0.5*V_mean*h-(dp|dr*(h^3)/(12*μ_viscosity))
This formula uses 5 Variables

Variables Used

Rate of Flow - (Measured in Cubic Meter per Second) - Rate of Flow is the rate at which a liquid or other substance flows through a particular channel, pipe, etc.
Mean Velocity - (Measured in Meter per Second) - Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.
Height - (Measured in Meter) - Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.
Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external 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: 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_flow = 0.5*V_mean*h-(dp|dr*(h^3)/(12*μ_viscosity)) --> 0.5*10*1.81-(17*(1.81^3)/(12*1.02))

Evaluating ... ...

q_flow = 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 <-- Rate of Flow

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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Dynamic Viscosity given Pressure Gradient

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

Pressure Gradient

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

Rate of Flow given Pressure Gradient

Go Rate of Flow = 0.5*Mean Velocity*Height-(Pressure Gradient*(Height^3)/(12*Dynamic Viscosity))

Rate of Flow given Pressure Gradient Formula

Rate of Flow = 0.5*Mean Velocity*Height-(Pressure Gradient*(Height^3)/(12*Dynamic Viscosity))
q_flow = 0.5*V_mean*h-(dp|dr*(h^3)/(12*μ_viscosity))

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 Rate of Flow given Pressure Gradient?

Rate of Flow given Pressure Gradient calculator uses Rate of Flow = 0.5*Mean Velocity*Height-(Pressure Gradient*(Height^3)/(12*Dynamic Viscosity)) to calculate the Rate of Flow, Rate of Flow given Pressure Gradient is defined as the amount of fluid flow through component. Rate of Flow is denoted by q_flow 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 (h), Pressure Gradient (dp|dr) & Dynamic Viscosity (μ_viscosity) 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?

Rate of Flow given Pressure Gradient is defined as the amount of fluid flow through component and is represented as q_flow = 0.5*V_mean*h-(dp|dr*(h^3)/(12*μ_viscosity)) or Rate of Flow = 0.5*Mean Velocity*Height-(Pressure Gradient*(Height^3)/(12*Dynamic Viscosity)). Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T, Height is the distance between the lowest and highest points of a person/ shape/ object standing upright, Pressure Gradient is the change in pressure with respect to radial distance of element & The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.

How to calculate Rate of Flow given Pressure Gradient?

Rate of Flow given Pressure Gradient is defined as the amount of fluid flow through component is calculated using Rate of Flow = 0.5*Mean Velocity*Height-(Pressure Gradient*(Height^3)/(12*Dynamic Viscosity)). To calculate Rate of Flow given Pressure Gradient, you need Mean Velocity (V_mean), Height (h), Pressure Gradient (dp|dr) & Dynamic Viscosity (μ_viscosity). With our tool, you need to enter the respective value for Mean Velocity, Height, 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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