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Pressure Gradient given Rate of Flow Formula

GoPressure Gradient given Velocity of Flow in Oil Tank Formula

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Pressure Gradient is the change in pressure with respect to radial distance of element. Check FAQs

dp|dr = (12 \cdot \frac{μ}{{C R}^{3}}) \cdot ((\frac{Q}{π} \cdot D) + v piston \cdot 0.5 \cdot C R)

dp|dr - Pressure Gradient?μ - Dynamic Viscosity?C_R - Radial Clearance?Q - Discharge in Laminar Flow?D - Diameter of Piston?v_piston - Velocity of Piston?π - Archimedes' constant?

Pressure Gradient given Rate of Flow Example

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Here is how the Pressure Gradient given Rate of Flow equation looks like with Values.

Here is how the Pressure Gradient given Rate of Flow equation looks like with Units.

Here is how the Pressure Gradient given Rate of Flow equation looks like.

8231.8319 = (12 \cdot \frac{10.2}{{0.45}^{3}}) \cdot ((\frac{55}{3.1416} \cdot 3.5) + 0.045 \cdot 0.5 \cdot 0.45)

8231.8319N/m³ = (12 \cdot \frac{10.2P}{{0.45m}^{3}}) \cdot ((\frac{55m³/s}{3.1416} \cdot 3.5m) + 0.045m/s \cdot 0.5 \cdot 0.45m)

8231.8319 = (12 \cdot \frac{10.2}{{0.45}^{3}}) \cdot ((\frac{55}{3.1416} \cdot 3.5) + 0.045 \cdot 0.5 \cdot 0.45)

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Pressure Gradient given Rate of Flow Solution

Follow our step by step solution on how to calculate Pressure Gradient given Rate of Flow?

FIRST Step Consider the formula

dp|dr = (12 \cdot \frac{μ}{{C R}^{3}}) \cdot ((\frac{Q}{π} \cdot D) + v piston \cdot 0.5 \cdot C R)

Next Step Substitute values of Variables

∴

dp|dr = (12 \cdot \frac{10.2P}{{0.45m}^{3}}) \cdot ((\frac{55m³/s}{π} \cdot 3.5m) + 0.045m/s \cdot 0.5 \cdot 0.45m)

Next Step Substitute values of Constants

∴

dp|dr = (12 \cdot \frac{10.2P}{{0.45m}^{3}}) \cdot ((\frac{55m³/s}{3.1416} \cdot 3.5m) + 0.045m/s \cdot 0.5 \cdot 0.45m)

Next Step Convert Units

∴

dp|dr = (12 \cdot \frac{1.02Pa*s}{{0.45m}^{3}}) \cdot ((\frac{55m³/s}{3.1416} \cdot 3.5m) + 0.045m/s \cdot 0.5 \cdot 0.45m)

Next Step Prepare to Evaluate

∴

dp|dr = (12 \cdot \frac{1.02}{{0.45}^{3}}) \cdot ((\frac{55}{3.1416} \cdot 3.5) + 0.045 \cdot 0.5 \cdot 0.45)

Next Step Evaluate

∴

dp|dr = 8231.83192127569N/m³

LAST Step Rounding Answer

∴

dp|dr = 8231.8319N/m³

Pressure Gradient given Rate of Flow Formula Elements

Variables

Constants

Pressure Gradient

Pressure Gradient is the change in pressure with respect to radial distance of element.

Symbol: dp|dr

Measurement: Pressure GradientUnit: N/m³

Note: Value can be positive or negative.

Formulas to find Pressure Gradient

Dynamic Viscosity

The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.

Symbol: μ

Measurement: Dynamic ViscosityUnit: P

Note: Value should be greater than 0.

Formulas to find Dynamic Viscosity

Radial Clearance

Radial Clearance or gap is the distance between two surfaces adjacent to each other.

Symbol: C_R

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radial Clearance

Discharge in Laminar Flow

The Discharge in Laminar Flow refers to the fluid flowing per second through a channel or section of a pipe.

Symbol: Q

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Formulas to find Discharge in Laminar Flow

Diameter of Piston

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.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter of Piston

Velocity of 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.

Symbol: v_piston

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity of Piston

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Pressure Gradient

Go Pressure Gradient given Velocity of Flow in Oil Tank

dp|dr = \frac{μ \cdot 2 \cdot (u Oiltank - (v piston \cdot \frac{R}{C H}))}{R \cdot R - C H \cdot R}

Other formulas in Dash Pot Mechanism category

Go Velocity of Flow in Oil Tank

u Oiltank = (dp|dr \cdot 0.5 \cdot \frac{R \cdot R - C H \cdot R}{μ}) - (v piston \cdot \frac{R}{C H})

Go Pressure Drop over Piston

ΔPf = (6 \cdot μ \cdot v piston \cdot \frac{L P}{{C R}^{3}}) \cdot (0.5 \cdot D + C R)

Go Length of Piston for Pressure Drop over Piston

L P = \frac{ΔPf}{(6 \cdot μ \cdot \frac{v piston}{{C R}^{3}}) \cdot (0.5 \cdot D + C R)}

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

ΔPf = \frac{F v}{0.25 \cdot π \cdot D \cdot D}

How to Evaluate Pressure Gradient given Rate of Flow?

Pressure Gradient given Rate of Flow evaluator 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 evaluate 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 evaluate Pressure Gradient given Rate of Flow using this online evaluator? To use this online evaluator for Pressure Gradient given Rate of Flow, enter Dynamic Viscosity (μ), Radial Clearance (C_R), Discharge in Laminar Flow (Q), Diameter of Piston (D) & Velocity of Piston (v_piston) and hit the calculate button.

FAQs on Pressure Gradient given Rate of Flow

What is the formula to find Pressure Gradient given Rate of Flow?

The formula of Pressure Gradient given Rate of Flow is expressed as Pressure Gradient = (12*Dynamic Viscosity/(Radial Clearance^3))*((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance). Here is an example- 53.73573 = (12*1.02/(0.45^3))*((55/pi*3.5)+0.045*0.5*0.45).

How to calculate Pressure Gradient given Rate of Flow?

With Dynamic Viscosity (μ), Radial Clearance (C_R), Discharge in Laminar Flow (Q), Diameter of Piston (D) & Velocity of Piston (v_piston) we can find Pressure Gradient given Rate of Flow using the formula - Pressure Gradient = (12*Dynamic Viscosity/(Radial Clearance^3))*((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance). This formula also uses Archimedes' constant .

What are the other ways to Calculate Pressure Gradient?

Here are the different ways to Calculate Pressure Gradient-

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)

Can the Pressure Gradient given Rate of Flow be negative?

Yes, the Pressure Gradient given Rate of Flow, measured in Pressure Gradient can be negative.

Which unit is used to measure Pressure Gradient given Rate of Flow?

Pressure Gradient given Rate of Flow is usually measured using the Newton per Cubic Meter[N/m³] for Pressure Gradient. Newton per Cubic Inch[N/m³], Kilonewton per Cubic Kilometer[N/m³], Newton per Cubic Kilometer[N/m³] are the few other units in which Pressure Gradient given Rate of Flow can be measured.

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Pressure Gradient given Rate of Flow Formula

​GoPressure Gradient given Velocity of Flow in Oil Tank Formula

Pressure Gradient given Rate of Flow Example

Pressure Gradient given Rate of Flow Solution

Pressure Gradient given Rate of Flow Formula Elements

Other Formulas to find Pressure Gradient

Other formulas in Dash Pot Mechanism category

How to Evaluate Pressure Gradient given Rate of Flow?

FAQs on Pressure Gradient given Rate of Flow

Variable Name

GoPressure Gradient given Velocity of Flow in Oil Tank Formula