Chemical Engineering - Fluid Mechanics - Discussion
Discussion Forum : Fluid Mechanics - Section 1 (Q.No. 31)
31.
The drag co-efficient for a bacterium moving in water at 1 mm/s, will be of the following order of magnitude (assume size of the bacterium to be 1 micron and kinematic viscosity of water to be 10-6m2/s).
Discussion:
24 comments Page 1 of 3.
TANMAY SHAH said:
2 years ago
Nre = d * v * ρ / μ
d = 1 micron = 10^-6 meter
v = 1 mm/s = 10^-3 m/s
ρ = 10^3 kg/m3
μ = 10^-6 × 1000 = 10^-3 kg/m.s
[ because; dynamic μ = kinematic μ × ρ ]
Nre = 10^-6 × 10^-3 × 10^3 /10^-3.
Nre = 10^-3 = 0.001.
Now for Nre < 1 it is called laminar flow region.
In the laminar flow region, called the Stokes law region the drag coefficient,
Cd= 24 µ/d ρ ν = 24 / Nre
Cd = 24/0.001 = 24000.
So, option-A is the right answer.
d = 1 micron = 10^-6 meter
v = 1 mm/s = 10^-3 m/s
ρ = 10^3 kg/m3
μ = 10^-6 × 1000 = 10^-3 kg/m.s
[ because; dynamic μ = kinematic μ × ρ ]
Nre = 10^-6 × 10^-3 × 10^3 /10^-3.
Nre = 10^-3 = 0.001.
Now for Nre < 1 it is called laminar flow region.
In the laminar flow region, called the Stokes law region the drag coefficient,
Cd= 24 µ/d ρ ν = 24 / Nre
Cd = 24/0.001 = 24000.
So, option-A is the right answer.
(10)
Ashnu said:
1 decade ago
Correct answer is 24000. Because the range of motion of the particle is in stoke's law regime. Nre = 1x10-3 which is under stoke's law. Also Cd = b1/Nre^n where b1= 24 and n=1 for stoke's law.
Calculating all must result to 24000.
Calculating all must result to 24000.
Dhanush P said:
1 decade ago
Cd=(24/Re), applies only when Re < 1(according to stokes law).
When Re>1000, newtons law applies, where Cd is almost constant. i.e 0.44.
When Re>1000, newtons law applies, where Cd is almost constant. i.e 0.44.
Makda said:
6 years ago
The correct answer is 24000 because Re = 1000(please make sure dimensional similarly ;i.e 1micron = 10-6 and 1mm = 0.001m.
Lovakumar said:
1 decade ago
Cd = 24/Re for laminar.
Re = d*v/kine viscosity = 1000.
Since it is turbulent Cd = 0.44 which is constant for turbulent.
Re = d*v/kine viscosity = 1000.
Since it is turbulent Cd = 0.44 which is constant for turbulent.
Laxmi said:
9 years ago
In the Stokes Regime.
Cd = 24/Re.
But here since flow is turbulent, Re= 1000 So, Cd is almost constant and is 0.44.
Cd = 24/Re.
But here since flow is turbulent, Re= 1000 So, Cd is almost constant and is 0.44.
Paresh chaudhary said:
1 decade ago
Drag force cd = 24/Nre
Nre=dia*velocity/kinematic viscosity
= 24/.001
= 24000
Nre=dia*velocity/kinematic viscosity
= 24/.001
= 24000
Amit said:
5 years ago
Nre = D*V/ν = 10^-6*10^-3/10^6=10^-3=0.001. SO IT IS UNDER STOKES LAW.
SO CD = 24/Nre = 24/0.001=24000.
SO CD = 24/Nre = 24/0.001=24000.
Afeefa said:
1 decade ago
The Reynolds number is coming as (10^-3), and in stokes law regime cd=24/NRe which comes to be 24000.
Vikash lamoria said:
1 decade ago
Answer is 24000.
Cd = 24/Re for Reynold no.<1 and Re = .001.
So answer is 24000.
Cd = 24/Re for Reynold no.<1 and Re = .001.
So answer is 24000.
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