Engine oil (η = 0.20 pa⋅s) passes through a fine 1.90-mm-diameter tube that is 9.40cm long. what pressure difference is needed to maintain a flow rate of 6.4ml/min ? ,

In this problem which involves pressure difference  and flow  rate, you can use the formula:

Q = πPr^4/(8lη) 

Where:
Q = Flow in Liters/second 
η= Viscosity in Pa.s 
P = Pressure in pascals 
r = Radius of the tube in meters 
l = Length of the tube in meters 
The given needed to be converted to the right units for the formula.

Q = 6.4 mL/minute or (0.0064 /60) Liters /second 
η= 0.2 Pa.s 
r = 0.95 mm or 0.00095 m
l = 9.40 cm or 0.094 m

(0.0064/60) = π P (0.00095) ^4 /(8 x 0.094 x 0.2) 

The pressure difference can be found by solving for P in the equation.

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