How to Calculate and Solve for Velocity of Newtonian Fluid | Transport Phenomena

The image above represents the velocity of Newtonian fluid. To calculate the velocity of Newtonian fluid, five essential parameters are needed, and these parameters are Change in Pressure (ΔP), Distance between Fluid Flow (L), Diameter of Pipe (y), Separation Distance of Atoms (δ) and Viscosity (η).

The formula for calculating the velocity of Newtonian fluid:

v = ^{(δ² – y²)ΔP} / _2η.L

Where:

v = Velocity of Newtonian Fluid
ΔP = Change in Pressure
L = Distance between Fluid Flow
y = Diameter of Pipe
δ = Separation Distance of Atoms
η = Viscosity

Let’s solve an example;
Find the velocity of newtonian fluid when the change in pressure is 22, the distance between fluid flow is 13, the diameter of pipe is 7, the separation distance of atoms is 11 and the viscosity is 5.

This implies that;

ΔP = Change in Pressure = 22
L = Distance between Fluid Flow = 13
y = Diameter of Pipe = 7
δ = Separation Distance of Atoms = 11
η = Viscosity = 5

v = ^{(δ² – y²)ΔP} / _2η.L
That is, v = ^{(11² – 7²)22} / _2(5).(13)
v = ^{(121 – 49)22} / _(10).(13)
v = ⁽⁷²⁾²² / ₁₃₀
So, v = ¹⁵⁸⁴ / ₁₃₀
v = 12.18

Therefore, the velocity of newtonian fluid is 12.18 m/s.

Calculating the Change in Pressure when the Velocity of Newtonian Fluid, the Distance between Fluid Flow, the Diameter of Pipe, the Separation Distance of Atoms and the Viscosity are Given

ΔP = ^{v x 2η.L} / _{(δ² – y²)}

Where:

ΔP = Change in Pressure
v = Velocity of Newtonian Fluid
L = Distance between Fluid Flow
y = Diameter of Pipe
δ = Separation Distance of Atoms
η = Viscosity

Let’s solve an example;
Find the change in pressure when the velocity of newtonian fluid is 4, the distance between fluid flow is 2, the diameter of pipe is 3, the separation distance of atoms is 8 and the viscosity is 6.

This implies that;

v = Velocity of Newtonian Fluid = 4
L = Distance between Fluid Flow = 2
y = Diameter of Pipe = 3
δ = Separation Distance of Atoms = 8
η = Viscosity = 6

ΔP = ^{v x 2η.L} / _{(δ² – y²)}
ΔP = ^{4 x 2(6).(2)} / _{(8² – 3²)}
So, ΔP = ^{4 x 24} / _{(64 – 9)}
ΔP = ⁹⁶ / ₅₅
ΔP = 1.745

Therefore, the change in pressure is 1.745.

Read more: How to Calculate and Solve for Viscosity of Newtonian Fluids | Rheology

Calculating the Distance between Fluid Flow when the Velocity of Newtonian Fluid, the Change in Pressure, the Diameter of Pipe, the Separation Distance of Atoms and the Viscosity are Given

L = ^{(δ² – y²)ΔP} / _{v x 2η}

Where:

L = Distance between Fluid Flow
v = Velocity of Newtonian Fluid
ΔP = Change in Pressure
y = Diameter of Pipe
δ = Separation Distance of Atoms
η = Viscosity

Let’s solve an example;
Find the distance between fluid flow when the velocity of newtonian fluid is 10, the change in pressure is 4, the diameter of pipe is 1, the separation distance of atoms is 2 and the viscosity is 7.

This implies that;

v = Velocity of Newtonian Fluid = 10
ΔP = Change in Pressure = 4
y = Diameter of Pipe = 1
δ = Separation Distance of Atoms = 2
η = Viscosity = 7

L = ^{(δ² – y²)ΔP} / _{v x 2η}
L = ^{(2² – 1²)4} / _{10 x 2(7)}
That is, L = ^{(4 – 1)4} / _{10 x 14}
L = ¹² / ₁₄₀
L = 0.0857

Therefore, the distance between fluid flow is 0.0857 m.

Calculating the Diameter of Pipe when the Velocity of Newtonian Fluid, the Change in Pressure, the Distance between Fluid Flow, the Separation Distance of Atoms and the Viscosity are Given

y = √δ² – (^{v x 2η.L} / _ΔP)

Where:

y = Diameter of Pipe
v = Velocity of Newtonian Fluid
ΔP = Change in Pressure
L = Distance between Fluid Flow
δ = Separation Distance of Atoms
η = Viscosity

Let’s solve an example;
Find the diameter of pipe when the velocity of newtonian fluid is 3, the change in pressure is 5, the distance between fluid flow is 7, the separation distance of atoms is 24 and the viscosity is 11.

This implies that;

v = Velocity of Newtonian Fluid = 3
ΔP = Change in Pressure = 5
L = Distance between Fluid Flow = 7
δ = Separation Distance of Atoms = 24
η = Viscosity = 11

y = √δ² – (^{v x 2η.L} / _ΔP)
That is, y = √24² – (^{3 x 2(11).(7)} / ₅)
y = √576 – (⁴⁶² / ₅)
y = √576 – 92.4
So, y = √483.6
y = 21.99

Therefore, the diameter of pipe is 21.99 m.

Read more: How to Calculate and Solve for Non-Newtonian Fluid Shear Stress | Transport Phenomena

Calculating the Separation Distance of Atoms when the Velocity of Newtonian Fluid, the Change in Pressure, the Distance between Fluid Flow, the Diameter of Pipe and the Viscosity are Given

δ = √(^{v x 2η.L} / _ΔP) + y²

Where:

δ = Separation Distance of Atoms
v = Velocity of Newtonian Fluid
ΔP = Change in Pressure
L = Distance between Fluid Flow
y = Diameter of Pipe
η = Viscosity

Let’s solve an example;
Find the separation distance of atoms when the velocity of newtonian fluid is 12, the change in pressure is 10, the distance between fluid flow is 14, the diameter of pipe is 6 and the viscosity is 8.

v = Velocity of Newtonian Fluid = 12
ΔP = Change in Pressure = 10
L = Distance between Fluid Flow = 14
y = Diameter of Pipe = 6
η = Viscosity = 8

δ = √(^{v x 2η.L} / _ΔP) + y²
Then, δ = √(^{12 x 2(8).(14)} / ₁₀) + 6²
δ = √(²⁶⁸⁸ / ₁₀) + 36
δ = √268.8 + 36
That is, δ = √304.8
δ = 17.45

Therefore, the separation distance atoms is 17.45.

Calculating the Viscosity when the Velocity of Newtonian Fluid, the Change in Pressure, the Distance between Fluid Flow, the Diameter of Pipe and the Separation Distance of Atoms are Given

η = ^{(δ² – y²)ΔP} / _{v x 2η.L}

Where:

η = Viscosity
v = Velocity of Newtonian Fluid
ΔP = Change in Pressure
L = Distance between Fluid Flow
y = Diameter of Pipe
δ = Separation Distance of Atoms

Let’s solve an example;
Find the viscosity when the velocity of newtonian fluid is 22, the change in pressure is 6, the distance between fluid flow is 10, the diameter of pipe is 3 and the separation distance of atoms is 4.

This implies that;

v = Velocity of Newtonian Fluid = 22
ΔP = Change in Pressure = 6
L = Distance between Fluid Flow = 10
y = Diameter of Pipe = 3
δ = Separation Distance of Atoms = 4

η = ^{(δ² – y²)ΔP} / _{v x 2.L}
That is, η = ^{(4² – 3²)6} / _{22 x 2.(10)}
η = ^{(16 – 9)6} / ₄₄₀
η = ⁽⁷⁾⁶ / ₄₄₀
So, η = ⁴² / ₄₄₀
η = 0.095

Therefore, the viscosity is 0.095.

Read more: How to Calculate and Solve for Viscosity | Non Polar Gases | Transport Phenomena

How to Calculate the Velocity of Newtonian Fluid With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the velocity of newtonian fluid.

Now, Click on Transport Phenomena under Materials and Metallurgical

Now, Click on Velocity of Newtonian Fluid under Transport Phenomena

The screenshot below displays the page or activity to enter your values, to get the answer for the velocity of newtonian fluid according to the respective parameter which is the Change in Pressure (ΔP), Distance between Fluid Flow (L), Diameter of Pipe (y), Separation Distance of Atoms (δ) and Viscosity (η).

Now, enter the values appropriately and accordingly for the parameters as required by the Change in Pressure (ΔP) is 22, Distance between Fluid Flow (L) is 13, Diameter of Pipe (y) is 7, Separation Distance of Atoms (δ) is 11 and Viscosity (η) is 5.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the velocity of newtonian fluid and presents the formula, workings and steps too.