Pressure Gradient given Velocity of Fluid Calculator

✖Fluid Velocity in Oil Tank is the volume of fluid flowing in the given vessel per unit cross sectional area.ⓘ Fluid Velocity in Oil Tank [u_Oiltank]			+10% -10%
✖Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.ⓘ Horizontal Distance [R]			+10% -10%
✖Hydraulic Clearance is the gap or space between two surfaces adjacent to each other.ⓘ Hydraulic Clearance [C_H]			+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%

✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradient given Velocity of Fluid [dp|dr]

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Formula

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Pressure Gradient given Velocity of Fluid

Formula

`"dp|dr" = "u"_{"Oiltank"}/(0.5*("R"*"R"-"C"_{"H"}*"R")/"μ"_{"viscosity"})`

Example

`"53.8022N/m³"="12m/s"/(0.5*("0.7m"*"0.7m"-"50mm"*"0.7m")/"10.2P")`

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Pressure Gradient given Velocity of Fluid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Gradient = Fluid Velocity in Oil Tank/(0.5*(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance)/Dynamic Viscosity)
dp|dr = u_Oiltank/(0.5*(R*R-C_H*R)/μ_viscosity)
This formula uses 5 Variables

Variables Used

Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
Fluid Velocity in Oil Tank - (Measured in Meter per Second) - Fluid Velocity in Oil Tank is the volume of fluid flowing in the given vessel per unit cross sectional area.
Horizontal Distance - (Measured in Meter) - Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.
Hydraulic Clearance - (Measured in Meter) - Hydraulic Clearance is the gap or space between two surfaces adjacent to each other.
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

Fluid Velocity in Oil Tank: 12 Meter per Second --> 12 Meter per Second No Conversion Required
Horizontal Distance: 0.7 Meter --> 0.7 Meter No Conversion Required
Hydraulic Clearance: 50 Millimeter --> 0.05 Meter (Check conversion here)
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

dp|dr = u_Oiltank/(0.5*(R*R-C_H*R)/μ_viscosity) --> 12/(0.5*(0.7*0.7-0.05*0.7)/1.02)

Evaluating ... ...

dp|dr = 53.8021978021978

STEP 3: Convert Result to Output's Unit

53.8021978021978 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

53.8021978021978 ≈ 53.8022 Newton per Cubic Meter <-- Pressure Gradient

(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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< 14 When Piston Velocity is Negligible to Average Velocity of Oil in Clearance Space Calculators

Dynamic Viscosity given velocity of piston

Go Dynamic Viscosity = Total Force in Piston/(pi*Velocity of Piston*Piston Length*(0.75*((Diameter of Piston/Radial Clearance)^3)+1.5*((Diameter of Piston/Radial Clearance)^2)))

Pressure Gradient given Velocity of Fluid

Go Pressure Gradient = Fluid Velocity in Oil Tank/(0.5*(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance)/Dynamic Viscosity)

Velocity of Fluid

Go Fluid Velocity in Oil Tank = Pressure Gradient*0.5*(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance)/Dynamic Viscosity

Length of Piston for Pressure Reduction over Length of Piston

Go Piston Length = Pressure Drop due to Friction/((6*Dynamic Viscosity*Velocity of Piston/(Radial Clearance^3))*(0.5*Diameter of Piston))

Dynamic Viscosity for Pressure Drop over Length

Go Dynamic Viscosity = Pressure Drop due to Friction/((6*Velocity of Piston*Piston Length/(Radial Clearance^3))*(0.5*Diameter of Piston))

Pressure Drop over Lengths of Piston

Go Pressure Drop due to Friction = (6*Dynamic Viscosity*Velocity of Piston*Piston Length/(Radial Clearance^3))*(0.5*Diameter of Piston)

Velocity of Piston for Pressure reduction over Length of Piston

Go Velocity of Piston = Pressure Drop due to Friction/((3*Dynamic Viscosity*Piston Length/(Radial Clearance^3))*(Diameter of Piston))

Diameter of Piston for Pressure Drop over Length

Go Diameter of Piston = (Pressure Drop due to Friction/(6*Dynamic Viscosity*Velocity of Piston*Piston Length/(Radial Clearance^3)))*2

Dynamic Viscosity given Velocity of Fluid

Go Dynamic Viscosity = Pressure Gradient*0.5*((Horizontal Distance^2-Hydraulic Clearance*Horizontal Distance)/Fluid Velocity in Pipe)

Clearance given Pressure Drop over Length of Piston

Go Radial Clearance = (3*Diameter of Piston*Dynamic Viscosity*Velocity of Piston*Piston Length/Pressure Drop due to Friction)^(1/3)

Dynamic Viscosity given Shear Stress in Piston

Go Dynamic Viscosity = Shear Stress/(1.5*Diameter of Piston*Velocity of Piston/(Hydraulic Clearance*Hydraulic Clearance))

Velocity of Piston given Shear Stress

Go Velocity of Piston = Shear Stress/(1.5*Diameter of Piston*Dynamic Viscosity/(Hydraulic Clearance*Hydraulic Clearance))

Diameter of Piston given Shear Stress

Go Diameter of Piston = Shear Stress/(1.5*Dynamic Viscosity*Velocity of Piston/(Hydraulic Clearance*Hydraulic Clearance))

Clearance given Shear Stress

Go Hydraulic Clearance = sqrt(1.5*Diameter of Piston*Dynamic Viscosity*Velocity of Piston/Shear Stress)

Pressure Gradient given Velocity of Fluid Formula

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.

How to Calculate Pressure Gradient given Velocity of Fluid?

Pressure Gradient given Velocity of Fluid calculator uses Pressure Gradient = Fluid Velocity in Oil Tank/(0.5*(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance)/Dynamic Viscosity) to calculate the Pressure Gradient, The Pressure Gradient given Velocity of Fluid is defined as change in pressure with respect to distance in pipe. Pressure Gradient is denoted by dp|dr symbol.

How to calculate Pressure Gradient given Velocity of Fluid using this online calculator? To use this online calculator for Pressure Gradient given Velocity of Fluid, enter Fluid Velocity in Oil Tank (u_Oiltank), Horizontal Distance (R), Hydraulic Clearance (C_H) & Dynamic Viscosity (μ_viscosity) and hit the calculate button. Here is how the Pressure Gradient given Velocity of Fluid calculation can be explained with given input values -> 1345.055 = 12/(0.5*(0.7*0.7-0.05*0.7)/1.02).

FAQ

What is Pressure Gradient given Velocity of Fluid?

The Pressure Gradient given Velocity of Fluid is defined as change in pressure with respect to distance in pipe and is represented as dp|dr = u_Oiltank/(0.5*(R*R-C_H*R)/μ_viscosity) or Pressure Gradient = Fluid Velocity in Oil Tank/(0.5*(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance)/Dynamic Viscosity). Fluid Velocity in Oil Tank is the volume of fluid flowing in the given vessel per unit cross sectional area, Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion, Hydraulic Clearance is the gap or space between two surfaces adjacent to each other & The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.

How to calculate Pressure Gradient given Velocity of Fluid?

The Pressure Gradient given Velocity of Fluid is defined as change in pressure with respect to distance in pipe is calculated using Pressure Gradient = Fluid Velocity in Oil Tank/(0.5*(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance)/Dynamic Viscosity). To calculate Pressure Gradient given Velocity of Fluid, you need Fluid Velocity in Oil Tank (u_Oiltank), Horizontal Distance (R), Hydraulic Clearance (C_H) & Dynamic Viscosity (μ_viscosity). With our tool, you need to enter the respective value for Fluid Velocity in Oil Tank, Horizontal Distance, Hydraulic Clearance & 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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