Question

1. Engine oil that is classified as SAE 5W-30 has a density of 859 kg/m3 and a viscosity of 6.60 Pa⋅s at a temperature of –30 °C.   The oil is poured through a funnel with a neck that is 10.0 cm long and 1.00 cm in diameter. By continually pouring oil from a jug, the level of the oil is kept at a height of 10.0 cm above the neck of the funnel.
(a) Calculate the pressure at the top of the neck of the funnel.   i.e. Calculate the pressure at a depth of 10.0 cm below the surface of the oil in the funnel.
(b) Calculate the volume flow rate of oil through the funnel.    Hint: You may assume that the viscous effects need only be considered along the length of the neck of the funnel.
(c) How long will it take to pour 1.00 litre of oil through the funnel?    Note: Your answer will be surprisingly large! (6.60 Pa⋅s is a very high viscosity.)

Answer 1

p = pgh p = 859 kg/m^3 g = 9.8 m/s^2 P-A = pg tiomes (10 times 10^-2) + P-atm = 859 times 9.8 times 10^-1 N/m^2 = 841.8 N/m^2 + P_atm = 841.8 + 101325 = 102166.8 N/m^2 P_B = P_atm = 101325 N/m^2 Volume flow rate. = Delta p/(8nL/pi r^4) according to prisenille's eq^n = (P_A - P_C) pi r^4/8nL = 841.8 times 22/7 times (1 times 10^-2)^4/8 times 6.6 times (10 times 10^-2) = 0.004 m^3/s Time taken for 1 litre oil through funnel is to be calculated. volume 1 litre of oil = 0.001 m^3 Man of 1 litre = 0.001 times 59 = 859 kg Hence time taken = 0.859/0.004 = 214.8 secs = 3.55 mins