A liquid having a specific gravity of 0.95 and a viscosity of 0.0012 Pas flows at 0.8 m/s in a 2 cm diameter pipe. Using the convention of this unit, how would you describe the flow? A. Laminar B. Need more information C. Turbulent D. Transition
Question
A liquid having a specific gravity of 0.95 and a viscosity of 0.0012 Pas flows at 0.8 m/s in a 2 cm diameter pipe. Using the convention of this unit, how would you describe the flow? A. Laminar B. Need more information C. Turbulent D. Transition
Solution
To determine the type of flow, we can use the Reynolds number, which is a dimensionless quantity used in fluid mechanics to indicate the flow regime of a fluid. It is defined as the ratio of inertial forces to viscous forces and is used to predict the onset of turbulence.
The Reynolds number (Re) is calculated using the formula:
Re = (Density * Velocity * Diameter) / Viscosity
However, in this case, we are given the specific gravity instead of the density. The specific gravity of a substance is the ratio of the density of the substance to the density of a reference substance (usually water at 4 degrees Celsius, which has a density of 1000 kg/m^3). So, we can calculate the density of the liquid as follows:
Density = Specific Gravity * Density of water = 0.95 * 1000 = 950 kg/m^3
Now, we can calculate the Reynolds number:
Re = (950 kg/m^3 * 0.8 m/s * 0.02 m) / 0.0012 Pas = 12666.67
The flow is considered to be:
- Laminar if Re < 2000
- Transitional if 2000 < Re < 4000
- Turbulent if Re > 4000
So, with a Reynolds number of 12666.67, the flow would be described as turbulent. Therefore, the answer is C. Turbulent.
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