Glycerine flows steadily through a horizontal tube of length 1.5 m and

1.	Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is 4.0 x 10-3 kg s-1, what is the pressure difference between the two ends of the tube? (Density of glycerine = 1.3 x 103 kg m-3 and viscosity of glycerine = 0.83 Pa s). [You may also like to check if the assumption of laminar flow in the tube is correct.]
Answer» Here, l = 1.5 m, r = 1.0 cm = 1 x 10^-2 m Mass issuing out per second m = 4 x 10^-3 kg s^-1 ρ = 1.3 x 10³ kg m^-3 η = 0.83 Pa s Now volume issuing out per second V = m/ρ = {4 x 10^-3}/{1.3 x 10³}= 3.08 x 10^-6 m³ s^-1 Using Poiseulli's relation V = π/8 x pr⁴/ηl ⇒ p = 8 V ηl/πr⁴ = {8 x 3.08 x 10^-6 x 0.83 x 1.5}/{3.14 x (1 x 10^-2)⁴} = 976.97 Pa

Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is 4.0 x 10-3 kg s-1, what is the pressure difference between the two ends of the tube? (Density of glycerine = 1.3 x 103 kg m-3 and viscosity of glycerine = 0.83 Pa s). [You may also like to check if the assumption of laminar flow in the tube is correct.]

Answer»

Here, l = 1.5 m, r = 1.0 cm = 1 x 10^-2 m

Mass issuing out per second

m = 4 x 10^-3 kg s^-1

ρ = 1.3 x 10³ kg m^-3

η = 0.83 Pa s

Now volume issuing out per second

V = m/ρ = {4 x 10^-3}/{1.3 x 10³}= 3.08 x 10^-6 m³ s^-1

Using Poiseulli's relation

V = π/8 x pr⁴/ηl

⇒ p = 8 V ηl/πr⁴ = {8 x 3.08 x 10^-6 x 0.83 x 1.5}/{3.14 x (1 x 10^-2)⁴}

= 976.97 Pa