Engine oil at T = 60 °C is forced to flow between two very large, stationary, parallel flat plates separated by a thin gap height h = 3.60 mm. The plate dimensions are L = 1.25 m and W = 0.550 m. The outlet pressure is atmospheric, and the inlet pressure is 1 atm gage pressure.
Estimate the volume flow rate of oil. Also calculate the Reynolds number of the oil flow, based on gap height h and average velocity V.
Is the flow laminar or turbulent?

(a) The volume flow rate is 5.43 × 10⁻³ m³/s

(b) The Reynolds's number is 251.1

The flow is laminar as the Reynolds's number is below the critical value of 2040

Explanation:

Here, we have  

The engine oil temperature = 60 °C

Plate gap = 3.60 m

Plate dimensions =

Length, L = 1.25 m

Width, W = 0.550 m

Inlet pressure = 1 atm

Viscosity of engine oil at  SAE 10W - 60

μ = 31.946 mPa.s = 0.031946 kg/m·s

(a)

The rate of change of velocity is given by;

By substituting, we arrive at

The volume flow rate is

(b) The velocity, V is given by

, we plug in the values and we have;

Reynolds's number is given by;

Where, ρ for the engine oil is 0.8130 g/cm³ = 813 kg/m³

As the Reynolds's number value is less than 2040, the flow is laminar flow.

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