Concept #1: Flow & Continuity Equation

Example #1: Continuity / Proportional Reasoning

Practice: A cylindrical pipe with inner diameter of 4 cm is used to fill up a 10,000 L tank with a 700 kg/m^{3} oil. If it takes one hour to fill up the tank, calculate the speed, in m/s, with which the oil travels inside of the pipe.

A hose is connected to a faucet and used to fill a 7.0-L container in a time of 45 s. Determine the velocity of the water in the hose in the first part if it has a radius of 1 cm.

A cylindrical blood vessel is partially blocked by the buildup of plaque. At one point, the plaque decreases the diameter of the vessel by 65.0%. The blood approaching the blocked portion has speed v0 Just as the blood enters the blocked portion of the vessel, what will be its speed in terms of v0 ?

An incompressible fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?(A) 0.32 m/s(B) 0.64 m/s(C) 5.08 m/s(D) 2.56 m/s(E) 1.28 m/s

Compared to the speed of the water in the 0.5-cm pipe, the speed in the 1-cm pipe isa. one-quarter the speed in the 0.5-cm pipe.b. one-half the speed in the 0.5-cm pipe.c. the same as the speed in the 0.5-cm pipe.d. double the speed in the 0.5-cm pipe.e. quadruple the speed in the 0.5-cm pipe.

Blood flows through an artery that is partially blocked. As the blood moves from the wider region into the narrow region,the blood speed
a. increases.
b. decreases.
c. stays the same.
d. drops to zero.
e. alternately increases and then decreases.

An incompressible fluid is flowing through a horizontal tube which, at some point has a constriction such that the area of the tube becomes much smaller.
How do the fluid pressure and speed of flow compare at point B in the constricted region to their values at point A in the normal part of the tube?
A. The pressure and speed of flow are both much greater at point A than at point B.
B. The pressure and speed of flow are both much greater at point B than at point A.
C. At point B, the speed of flow is less but the pressure is greater than at point A.
D. Because the fluid is incompressible, the pressure and speed of flow must be constant throughout the tube.
E. At point A, the speed of flow is less but the pressure is greater than at point B.

A hose is connected to a faucet and used to fill a 7.0-L container in a time of 45 s. Determine the volume flow rate in m3/s. (Express your answer to two significant figures.)

You’re holding a hose at waist height and spraying water horizontally with it. The hose nozzle has a diameter of 1.80 cm, and the water splashes on the ground a distance of 0.950 m horizontally from the nozzle. Suppose you now constrict the nozzle to a diameter of 0.750 cm; how far horizontally from the nozzle will the water travel before hitting the ground? (Ignore air resistance.)

a) Calculate the mass flow rate (in grams per second) of blood (ρ = 1.0 g/cm 3) in an aorta with a cross-sectional area of 2.0 cm2 if the flow speed is 40 cm/s.b) Assume that the aorta branches to form a large number of capillaries with a combined cross-sectional area of 3.0 x 103 cm2. What is the flow speed in the capillaries?

The approximate diameter of the aorta is 0.50 cm; that of a capillary is 10 μm. The approximate average blood flow speed is 1.0 m/s in the aorta and 1.0 cm/s in the capillaries. If all the blood in the aorta eventually flows through the capillaries, estimate the number of capillaries in the circulatory system.