density

How to Calculate and Solve for Drag Force | Transport Phenomena

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The image above represents drag force.

To compute for drag force, five essential parameters are needed and these parameters are Density (ρ), Viscosity (η), Length of Tube (L), Width of Tube (W) and Velocity at Infinite Flow (v∞).

The formula for calculating drag force:

Fk = 0.664√(ρηLW²v∞³)

Where:

Fk = Drag Force
ρ = Density
η = Viscosity
L = Length of Tube
W = Width of Tube
v∞ = Velocity at Infinite Flow

Let’s solve an example;
If density is 10, the viscosity is 12, the length of tube is 16, the width of tube is 14 and the velocity at infinite flow is 11. Find the drag force?

This implies that;

ρ = Density = 10
η = Viscosity = 12
L = Length of Tube = 16
W = Width of Tube = 14
v∞ = Velocity at Infinite Flow = 11

Fk = 0.664√(ρηLW²v∞³)
Fk = 0.664√((10)(12)(16)(14)²(11)³)
Fk = 0.664√((10)(12)(16)(196)(1331))
Fk = 0.664√(500881920)
Fk = 0.664 (22380.39)
Fk = 14860.57

Therefore, the drag force is 14860.57 N.

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How to Calculate and Solve for Kinematic Viscosity | Transport Phenomena

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The image above represents kinematic viscosity.

To compute for kinematic viscosity, two essential parameters are needed and these parameters are Viscosity (η) and Density (ρ).

The formula for calculating kinematic viscosity:

V = η / ρ

Where:

V = Kinematic Viscosity
η = Viscosity
ρ = Density

Let’s solve an example;
Find the kinematic viscosity when the viscosity is 44 and the density is 11.

This implies that;

η = Viscosity = 44
ρ = Density = 11

V = η / ρ
V = 44 / 11
V = 4

Therefore, the kinematic viscosity is 4 m²/s.

Calculating the Viscosity when the Kinematic Viscosity and the Density is Given.

η = V x ρ

Where:

η = Viscosity
V = Kinematic Viscosity
ρ = Density

Let’s solve an example;
Find the viscosity when the kinematic viscosity is 10 and the density is 5.

This implies that;

V = Kinematic Viscosity = 10
ρ = Density = 5

η = V x ρ
η = 10 x 5
η = 50

Therefore, the viscosity is 50.

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How to Calculate and Solve for Speed of Sound throughout Liquid | Energy Transport

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The image above represents speed of sound throughout liquid.

To compute for speed of sound throughout liquid, four essential parameters are needed and these parameters are Heat Capacity at Constant Pressure (cp), Heat Capacity at Constant Volume (cv), Density (ρ) and Compressibility (β).

The formula for calculating the speed of sound throughout liquid:

vs = (cp / cvρβ)0.5

Where:

vs = Speed of Sound throughout Liquid
cp = Heat Capacity at Constant Pressure
cv = Heat Capacity at Constant Volume
ρ = Density
β = Compressibility

Let’s solve an example;
Find the speed of sound throughout liquid when the heat capacity at constant pressure is 12, the heat capacity at constant volume is 10, the density is 20 and the compressibility is 14.

This implies that;

cp = Heat Capacity at Constant Pressure = 12
cv = Heat Capacity at Constant Volume = 10
ρ = Density = 20
β = Compressibility = 14

vs = (cp / cvρβ)0.5
vs = (10 / (10)(20)(14))0.5
vs = (10 / 2800)0.5
vs = (0.00428)0.5
vs = 0.065

Therefore, the speed of sound throughout liquid is 0.065 m/s.

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How to Calculate and Solve for Thickness of Solidifying Metals | Solidification of Metals

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The image above represents thickness of solidifying metals.

To compute for thickness of solidifying metals, six essential parameters are needed and these parameters are Melting Temperature of Metal (Tm), Initial Mould Temperature (To), Heat Diffusivity (α), Time (t), Density (ρ’) and Latent Heat of Fusion (Hf).

The formula for calculating thickness of solidifying metals:

M = 2(Tm – To)√(α)√(t) / √(π)ρ’Hf

Where:

M = Thickness of Solidifying Metal
Tm = Melting Temperature of Metal
To = Initial Mould Temperature
α = Heat Diffusivity
t = Time
ρ = Density
Hf = Latent Heat of Fusion

Let’s solve an example;
Find the thickness of solidifying metal when the melting temperature of metal is 4, the initial mould temperature is 8, the heat diffusivity is 2, the time is 6, the density is 3 and the latent heat of fusion is 7.

This implies that;

Tm = Melting Temperature of Metal = 4
To = Initial Mould Temperature = 8
α = Heat Diffusivity = 2
t = Time = 6
ρ = Density = 3
Hf = Latent Heat of Fusion = 7

M = 2(Tm – To)√(α)√(t) / √(π)ρ’Hf
M = 2(4 – 8)√(2)√(6) / √(π)(3)(7)
M = 2(-4)(1.414)(2.449) / (1.772)(3)(7)
M = -27.712 / 37.22
M = -0.744

Therefore, the thickness of solidifying metal is -0.744 m.

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