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

Water flows through a horizontal tube of diameter 2.8 cm that is joined to a second horizontal tube of diameter 1.6 cm. The pressure difference, P1- P2, between the tubes is 7.5 kPa.
a) Which tube has the higher pressure?
b) Which tube has the higher speed of flow?
c) Find the speed of flow in the first (larger) tube.
d) Find the speed of flow in the second (smaller) tube.

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.

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.)

When the atmospheric pressure is 1.00 atm, a water fountain ejects a stream of water that rises to a height of 6.00 m. There is a 2.00-cm-radius pipe that leads from a pressurized tank to the opening that ejects the water. Assume that the atmospheric pressure is that of the eye of a hurricane, 0.877 atm, and the tank’s pressure remains the same. Calculate the new height if the fountain were operating when the eye of a hurricane passes through.

The Venturi meter is used to measure the speed of air (density ρa) and is shown in the figure below. It consists of a horizontal pipe with variable sectional areas, and a flexible hose, partially filled with water (density ρw), connecting two points in the pipe with different areas. Air enters the meter at speed v1 and atmospheric pressure po. The sectional area of the meter is A1 at point 1 and A2 at point 2.
a) What is the speed of the air at point 2?
b) What is the pressure of the air at point 2?
c) What is the value of h, the difference between the water levels at 3 and 4?
d) If the speed v1 doubles, how much bigger (or smaller) does h become?
Notice that h is not a given parameter of the problem.

When a person inhales, air moves down the bronchus (windpipe) at 16 cm/s. The average flow speed of the air doubles through a constriction in the bronchus. Assuming incompressible flow, find the pressure drop in the constriction. The density of air is 1.29 kg/m 3
1. 0.049536
2. 0.01935
3. 0.062694
4. 0.0559215
5. 0.0327015
6. 0.0435375
7. 0.0234135
8. 0.027864
9. 0.037926
10. 0.0698535

Water enters a tube of radius 5 cm at 10 m/s and a pressure of 10 5 Pa. After traveling through some piping, the water exits from a tube of radius 8 cm at a height of 10 m above whete it enters. At what pressure does the water exit the piping?