Pressure Gradient given Rate of Flow 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%
✖Radial Clearance or gap is the distance between two surfaces adjacent to each other.ⓘ Radial Clearance [C_R]			+10% -10%
✖Discharge in Laminar Flow is the fluid flowing per second through a channel or section of a pipe.ⓘ Discharge in Laminar Flow [Q]			+10% -10%
✖Diameter of Piston is the actual diameter of the piston while the bore is the size of the cylinder and will always be larger than the piston.ⓘ Diameter of Piston [D]			+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%

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

⎘ Copy

👎

Formula

✖

Pressure Gradient given Rate of Flow

Formula

`"dp|dr" = (12*"μ"_{"viscosity"}/("C"_{"R"}^3))*(("Q"/pi*"D")+"v"_{"piston"}*0.5*"C"_{"R"})`

Example

`"8231.832N/m³"=(12*"10.2P"/(("0.45m")^3))*(("55m³/s"/pi*"3.5m")+"0.045m/s"*0.5*"0.45m")`

Calculator

LaTeX

Reset

👍

Download Dash-Pot Mechanism Formulas PDF

Pressure Gradient given Rate of Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Gradient = (12*Dynamic Viscosity/(Radial Clearance^3))*((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance)
dp|dr = (12*μ_viscosity/(C_R^3))*((Q/pi*D)+v_piston*0.5*C_R)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
Radial Clearance - (Measured in Meter) - Radial Clearance or gap is the distance between two surfaces adjacent to each other.
Discharge in Laminar Flow - (Measured in Cubic Meter per Second) - Discharge in Laminar Flow is the fluid flowing per second through a channel or section of a pipe.
Diameter of Piston - (Measured in Meter) - Diameter of Piston is the actual diameter of the piston while the bore is the size of the cylinder and will always be larger than the piston.
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.

STEP 1: Convert Input(s) to Base Unit

Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Radial Clearance: 0.45 Meter --> 0.45 Meter No Conversion Required
Discharge in Laminar Flow: 55 Cubic Meter per Second --> 55 Cubic Meter per Second No Conversion Required
Diameter of Piston: 3.5 Meter --> 3.5 Meter No Conversion Required
Velocity of Piston: 0.045 Meter per Second --> 0.045 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

dp|dr = (12*μ_viscosity/(C_R^3))*((Q/pi*D)+v_piston*0.5*C_R) --> (12*1.02/(0.45^3))*((55/pi*3.5)+0.045*0.5*0.45)

Evaluating ... ...

dp|dr = 8231.83192127569

STEP 3: Convert Result to Output's Unit

8231.83192127569 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

8231.83192127569 ≈ 8231.832 Newton per Cubic Meter <-- Pressure Gradient

(Calculation completed in 00.020 seconds)

You are here -

Home » Engineering » Civil » Hydraulics and Waterworks » Laminar Flow » Dash-Pot Mechanism » Pressure Gradient given Rate of Flow

Credits

Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Calculator and 1300+ more calculators!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Calculator and 1700+ more calculators!

< 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 Rate of Flow 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 Rate of Flow?

Pressure Gradient given Rate of Flow calculator uses Pressure Gradient = (12*Dynamic Viscosity/(Radial Clearance^3))*((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance) to calculate the Pressure Gradient, The Pressure Gradient given Rate of Flow is defined as change in pressure with respect to horizontal distance in the piston flow. Pressure Gradient is denoted by dp|dr symbol.

How to calculate Pressure Gradient given Rate of Flow using this online calculator? To use this online calculator for Pressure Gradient given Rate of Flow, enter Dynamic Viscosity (μ_viscosity), Radial Clearance (C_R), Discharge in Laminar Flow (Q), Diameter of Piston (D) & Velocity of Piston (v_piston) and hit the calculate button. Here is how the Pressure Gradient given Rate of Flow calculation can be explained with given input values -> 53.73573 = (12*1.02/(0.45^3))*((55/pi*3.5)+0.045*0.5*0.45).

FAQ

What is Pressure Gradient given Rate of Flow?

The Pressure Gradient given Rate of Flow is defined as change in pressure with respect to horizontal distance in the piston flow and is represented as dp|dr = (12*μ_viscosity/(C_R^3))*((Q/pi*D)+v_piston*0.5*C_R) or Pressure Gradient = (12*Dynamic Viscosity/(Radial Clearance^3))*((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance). The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Radial Clearance or gap is the distance between two surfaces adjacent to each other, Discharge in Laminar Flow is the fluid flowing per second through a channel or section of a pipe, Diameter of Piston is the actual diameter of the piston while the bore is the size of the cylinder and will always be larger than the piston & Velocity of piston in reciprocating pump is defined as the product of sin of angular velocity and time, radius of crank and angular velocity.

How to calculate Pressure Gradient given Rate of Flow?

The Pressure Gradient given Rate of Flow is defined as change in pressure with respect to horizontal distance in the piston flow is calculated using Pressure Gradient = (12*Dynamic Viscosity/(Radial Clearance^3))*((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance). To calculate Pressure Gradient given Rate of Flow, you need Dynamic Viscosity (μ_viscosity), Radial Clearance (C_R), Discharge in Laminar Flow (Q), Diameter of Piston (D) & Velocity of Piston (v_piston). With our tool, you need to enter the respective value for Dynamic Viscosity, Radial Clearance, Discharge in Laminar Flow, Diameter of Piston & Velocity of Piston 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, Radial Clearance, Discharge in Laminar Flow, Diameter of Piston & Velocity of Piston. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

Home

FREE PDFs

🔍 Search