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Shown in the figure is a container whose top and bottom diameters are D and d respectively. At the bottom of the container. there is a capillary tube of outer radius b and inner radius a. The volume flow rate in the capillary is Q. If the capillary is removed the liquid comes out with a velocity of v ­0 . The density of the liquid is given as ρ. Calculate the coefficient of viscosity η.

Shown in the figure is a container whose top and bottom diameters are D and d respectively. At the bottom of the container. there is a capillary tube of outer radius b and inner radius a. 
The volume flow rate in the capillary is Q. If the capillary is removed the liquid comes out with a velocity of v­0. The density of the liquid is given as ρ. Calculate the coefficient of viscosity η. 

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
7 years ago
Hello Student,
Please find the answer to your question
KEY CONCEPT :
When the tube is not there, using Bernaoulli’s theorem
P + p0 + 1 / 2 ρv21 + ρgH = ½ pv20 + P0
⇒ P + ρgH = ½ p (v20 – v21)
But according to equation of continuity
Y1 = A2 v0 / A1
∴ P + ρgH = ½ ρ [v20 - (A2 / A1 v0)2]
P + ρgH = ½ ρv20 [1 – (A2 / A1)2]
Here, P + ρgH =∆P
According to Poisseuille’s equation
Q = π(∆P)a4 / 8ηl ⇒ η = π(∆P)a4 / 8Qℓ
∴ η = π (P+ ρgH)a4 / 8Qℓ = π / 8Qℓ x ½ ρv20 [1 – (A2 / A1)2] x a4
Where A2 / A1 = d2 / D2
Η = π /8Ql x ½ ρv20 [1 – d4 / D4] x a4
Thanks
Kevin Nash
askIITians Faculty

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