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.