Pressure Gradient given Velocity of Flow in Oil Tank Calculator

✖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%
✖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%
✖Velocity of piston in reciprocating pump is defined as the product of sin of angular velocity and time, radius of crank and angular velocity.ⓘ Velocity of Piston [v_piston]			+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%

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

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Formula

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Pressure Gradient given Velocity of Flow in Oil Tank

Formula

`"dp|dr" = ("μ"_{"viscosity"}*2*("u"_{"Oiltank"}-("v"_{"piston"}*"R"/"C"_{"H"})))/("R"*"R"-"C"_{"H"}*"R")`

Example

`"50.97758N/m³"=("10.2P"*2*("12m/s"-("0.045m/s"*"0.7m"/"50mm")))/("0.7m"*"0.7m"-"50mm"*"0.7m")`

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Pressure Gradient given Velocity of Flow in Oil Tank Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Gradient = (Dynamic Viscosity*2*(Fluid Velocity in Oil Tank-(Velocity of Piston*Horizontal Distance/Hydraulic Clearance)))/(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance)
dp|dr = (μ_viscosity*2*(u_Oiltank-(v_piston*R/C_H)))/(R*R-C_H*R)
This formula uses 6 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.
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.
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.
Velocity of Piston - (Measured in Meter per Second) - Velocity of piston in reciprocating pump is defined as the product of sin of angular velocity and time, radius of crank and angular velocity.
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.

STEP 1: Convert Input(s) to Base Unit

Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Fluid Velocity in Oil Tank: 12 Meter per Second --> 12 Meter per Second No Conversion Required
Velocity of Piston: 0.045 Meter per Second --> 0.045 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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

dp|dr = (μ_viscosity*2*(u_Oiltank-(v_piston*R/C_H)))/(R*R-C_H*R) --> (1.02*2*(12-(0.045*0.7/0.05)))/(0.7*0.7-0.05*0.7)

Evaluating ... ...

dp|dr = 50.9775824175824

STEP 3: Convert Result to Output's Unit

50.9775824175824 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

50.9775824175824 ≈ 50.97758 Newton per Cubic Meter <-- Pressure Gradient

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Laminar Flow » Dash-Pot Mechanism » Pressure Gradient given Velocity of Flow in Oil Tank

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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NSS College of Engineering (NSSCE), Palakkad

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< 12 Dash-Pot Mechanism Calculators

Pressure Gradient given Velocity of Flow in Oil Tank

Go Pressure Gradient = (Dynamic Viscosity*2*(Fluid Velocity in Oil Tank-(Velocity of Piston*Horizontal Distance/Hydraulic Clearance)))/(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance)

Velocity of Flow in Oil Tank

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

Length of Piston for Vertical Upward Force on Piston

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

Vertical Upward Force on Piston given Piston Velocity

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

Length of Piston for Shear Force Resisting Motion of Piston

Go Piston Length = Shear Force/(pi*Dynamic Viscosity*Velocity of Piston*(1.5*(Diameter of Piston/Radial Clearance)^2+4*(Diameter of Piston/Radial Clearance)))

Shear Force Resisting Motion of Piston

Go Shear Force = pi*Piston Length*Dynamic Viscosity*Velocity of Piston*(1.5*(Diameter of Piston/Radial Clearance)^2+4*(Diameter of Piston/Radial Clearance))

Pressure Gradient given Rate of Flow

Go Pressure Gradient = (12*Dynamic Viscosity/(Radial Clearance^3))*((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance)

Length of Piston for Pressure Drop over Piston

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

Pressure Drop over Piston

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

Pressure Drop over Length of Piston given Vertical Upward Force on Piston

Go Pressure Drop due to Friction = Vertical Component of Force/(0.25*pi*Diameter of Piston*Diameter of Piston)

Vertical Force given Total Force

Go Vertical Component of Force = Shear Force-Total Force in Piston

Total Forces

Go Total Force = Vertical Component of Force+Shear Force

Pressure Gradient given Velocity of Flow in Oil Tank 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 Flow in Oil Tank?

Pressure Gradient given Velocity of Flow in Oil Tank calculator uses Pressure Gradient = (Dynamic Viscosity*2*(Fluid Velocity in Oil Tank-(Velocity of Piston*Horizontal Distance/Hydraulic Clearance)))/(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance) to calculate the Pressure Gradient, The Pressure Gradient given Velocity of Flow in Oil Tank 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 Flow in Oil Tank using this online calculator? To use this online calculator for Pressure Gradient given Velocity of Flow in Oil Tank, enter Dynamic Viscosity (μ_viscosity), Fluid Velocity in Oil Tank (u_Oiltank), Velocity of Piston (v_piston), Horizontal Distance (R) & Hydraulic Clearance (C_H) and hit the calculate button. Here is how the Pressure Gradient given Velocity of Flow in Oil Tank calculation can be explained with given input values -> 1342.23 = (1.02*2*(12-(0.045*0.7/0.05)))/(0.7*0.7-0.05*0.7).

FAQ

What is Pressure Gradient given Velocity of Flow in Oil Tank?

The Pressure Gradient given Velocity of Flow in Oil Tank is defined as change in pressure with respect to distance in pipe and is represented as dp|dr = (μ_viscosity*2*(u_Oiltank-(v_piston*R/C_H)))/(R*R-C_H*R) or Pressure Gradient = (Dynamic Viscosity*2*(Fluid Velocity in Oil Tank-(Velocity of Piston*Horizontal Distance/Hydraulic Clearance)))/(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance). The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Fluid Velocity in Oil Tank is the volume of fluid flowing in the given vessel per unit cross sectional area, Velocity of piston in reciprocating pump is defined as the product of sin of angular velocity and time, radius of crank and angular velocity, 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.

How to calculate Pressure Gradient given Velocity of Flow in Oil Tank?

The Pressure Gradient given Velocity of Flow in Oil Tank is defined as change in pressure with respect to distance in pipe is calculated using Pressure Gradient = (Dynamic Viscosity*2*(Fluid Velocity in Oil Tank-(Velocity of Piston*Horizontal Distance/Hydraulic Clearance)))/(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance). To calculate Pressure Gradient given Velocity of Flow in Oil Tank, you need Dynamic Viscosity (μ_viscosity), Fluid Velocity in Oil Tank (u_Oiltank), Velocity of Piston (v_piston), Horizontal Distance (R) & Hydraulic Clearance (C_H). With our tool, you need to enter the respective value for Dynamic Viscosity, Fluid Velocity in Oil Tank, Velocity of Piston, Horizontal Distance & Hydraulic Clearance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Pressure Gradient?

In this formula, Pressure Gradient uses Dynamic Viscosity, Fluid Velocity in Oil Tank, Velocity of Piston, Horizontal Distance & Hydraulic Clearance. We can use 1 other way(s) to calculate the same, which is/are as follows -

Pressure Gradient = (12*Dynamic Viscosity/(Radial Clearance^3))*((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance)

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