Back(II) A viscometer consists of two concentric cylinders, 10.20 cm and 10.60 cm in diameter. A liquid fills the space between them to a depth of 15.0 cm. The outer cylinder is fixed, and a torque of 0.024 m N keeps the inner cylinder turning at a steady rotational speed of 57 rev/min. What is the viscosity of the liquid?
(I) Engine oil (assume SAE 10, Table 13–3) passes through a fine 1.80-mm-diameter tube that is 10.2 cm long. What pressure difference is needed to maintain a flow rate of 5.8 mL/min?
(II) Poiseuille’s equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, Re, exceeds approximately 2000. Re is defined as where is the average speed of the fluid, ρ is its density, is its viscosity, and r is the radius of the tube in which the fluid is flowing. Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta (r = 1.2 cm) during the resting part of the heart’s cycle is about 35 cm/s.
(III) A long vertical hollow tube with an inner diameter of 1.00 cm is filled with SAE 10 motor oil. A 0.900-cm-diameter, 30.0-cm-long 150-g rod is dropped vertically through the oil in the tube. What is the maximum speed attained by the rod as it falls?
A 12-cm-radius air duct is used to replenish the air of a room 8.2 m x 4.5 m x 3.5 m every 12 min. How fast does the air flow in the duct?
What is the volume rate of flow of water from a 1.85-cm-diameter faucet if the pressure head is 12.0 m?
How fast does water flow from a hole at the bottom of a very wide, 5.1-m-deep storage tank filled with water? Ignore viscosity.
A fire hose exerts a force on the person holding it due to the water accelerating as it goes from the thicker hose out through the narrow nozzle. How much force is required to hold a 7.0-cm-diameter hose delivering 480 L/min through a 0.75-cm-diameter nozzle?
(II) A 5/8 -in. (inside) diameter garden hose is used to fill a round swimming pool 6.1 m in diameter. How long will it take to fill the pool to a depth of 1.4 m if water flows from the hose at a speed of 0.40 m/s?
What must be the pressure difference between the two ends of a 1.6-km section of pipe, 29 cm in diameter, if it is to transport oil (ρ = 950 kg/m³, η=0.20 Pa⋅s) at a rate of 650 cm³/s?