Water flows in 2 cm dia pipe. The kinematic viscosity v=0.0098 stokes. Calculate the largest
discharge for which flow will be definitely laminar. what is the boundary shear stress at this
discharge. Take.p=1000 kg/m
Answers
Answer:
Discharge, Q = 2.27 m3/min=2.2760= 0.0378m3/s. kinematic viscosity,. v = 0.0098 stokes = 0.0098 cm2/s ... The flow is turbulent and Re is more than 10
Answer:
The biggest discharge for which the waft will be clearly laminar is
8.837 × 10⁻⁴ m³/s, and the boundary shear stress at this discharge is 0.026 Pa.
Explanation:
From the above question,
We have to calculate the largest discharge for which the flow will be definitely laminar Water flows in a 2 cm diameter pipe. Taking the kinematic viscosity of water as 0.0098 stoke, L/min
Here,
p = 1000 kg/m
To decide the biggest discharge for which the float in the pipe is in reality laminar, we can use the Reynolds number, which is described as:
Re = (ρVD)/μ
where ρ is the density of water, V is the common pace of the fluid, D is the diameter of the pipe, and μ is the dynamic viscosity of water.
For laminar flow, the Reynolds variety must be much less than 2300. Setting Re = 2300, we can remedy for the most speed V_max:
2300 = (ρV_maxD)/μ
V_max = (2300μ)/(ρD)
Now we can calculate the most drift rate, Q_max:
Q_max = A × V_max = (πD²/4) × V_max
where A is the cross-sectional place of the pipe.
Substituting the given values and solving, we get:
V_max = (2300 × 0.0098)/(1000 × 0.02) = 1.123 m/s
Q_max = (π × 0.02²/4) × 1.123 = 8.837 × 10⁻⁴ m³/s
To calculate the boundary shear stress at this discharge, we can use the formula:
τ_w = (4μQ)/(πD³)
where τ_w is the wall shear stress.
Substituting the given values, we get:
τ_w = (4 × 0.0098 × 8.837 × 10⁻⁴)/(π × 0.02³)
= 0.026 Pa
Hence,
The biggest discharge for which the waft will be clearly laminar is 8.837 × 10⁻⁴ m³/s, and the boundary shear stress at this discharge is 0.026 Pa.
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