Exercises: Continuity Equation
Water flows steadily through a horizontal pipe whose cross-sectional area is $0.020\ \text{m}^2$. The water moves at $1.5\ \text{m/s}$. Calculate the volume flow rate…
Water flows steadily through a horizontal pipe whose cross-sectional area is $0.020\ \text{m}^2$. The water moves at $1.5\ \text{m/s}$. Calculate the volume flow rate through the pipe in $\text{m}^3/\text{s}$.
State the continuity equation for an ideal, incompressible fluid flowing steadily through a pipe whose cross-sectional area changes from $A_1$ to $A_2$. Say what…
State the continuity equation for an ideal, incompressible fluid flowing steadily through a pipe whose cross-sectional area changes from $A_1$ to $A_2$. Say what physical quantity is conserved, and define each symbol you use.
A garden hose has a cross-sectional area of $2.0\times10^{-4}\ \text{m}^2$, and the water inside it moves at $0.50\ \text{m/s}$. Emma partly covers the end with her…
A garden hose has a cross-sectional area of $2.0\times10^{-4}\ \text{m}^2$, and the water inside it moves at $0.50\ \text{m/s}$. Emma partly covers the end with her thumb so that the opening has an area of $5.0\times10^{-5}\ \text{m}^2$. Find the speed of the water as it leaves the opening.
A pipe carries water with a radius of $0.050\ \text{m}$ in a wide section. It narrows to a radius of $0.020\ \text{m}$. The water speed in the wide section is…
A pipe carries water with a radius of $0.050\ \text{m}$ in a wide section. It narrows to a radius of $0.020\ \text{m}$. The water speed in the wide section is $1.2\ \text{m/s}$.
(a) Find the water speed in the narrow section.
(b) Find the volume flow rate in each section and compare them.
A town's water main delivers water at a volume flow rate of $0.080\ \text{m}^3/\text{s}$. A school's cylindrical tank has a base area of $12\ \text{m}^2$ and is filled…
A town's water main delivers water at a volume flow rate of $0.080\ \text{m}^3/\text{s}$. A school's cylindrical tank has a base area of $12\ \text{m}^2$ and is filled from this main with all of that flow. How long does it take the water level in the tank to rise by $1.5\ \text{m}$? Give your answer in seconds and in minutes.
Marcus watches a smooth stream of water fall from a kitchen faucet. He notices that the stream gets thinner as it falls. Using the continuity equation, explain why the…
Marcus watches a smooth stream of water fall from a kitchen faucet. He notices that the stream gets thinner as it falls. Using the continuity equation, explain why the stream narrows. Assume the flow is steady and the water speeds up as it falls.
A main pipe of cross-sectional area $0.040\ \text{m}^2$ carries water at $2.0\ \text{m/s}$. It splits into three identical branch pipes, each with a cross-sectional area…
A main pipe of cross-sectional area $0.040\ \text{m}^2$ carries water at $2.0\ \text{m/s}$. It splits into three identical branch pipes, each with a cross-sectional area of $0.010\ \text{m}^2$.
(a) Find the speed of the water in each branch.
(b) One branch is then shut off, and the main pipe keeps the same volume flow rate. Find the new speed in each of the two remaining branches.
(c) Explain, using conservation of mass, why the speed in the remaining branches changes.
A horizontal pipe has three sections in a row. Section A has diameter $0.30\ \text{m}$, section B has diameter $0.15\ \text{m}$, and section C has diameter…
A horizontal pipe has three sections in a row. Section A has diameter $0.30\ \text{m}$, section B has diameter $0.15\ \text{m}$, and section C has diameter $0.10\ \text{m}$. Water enters section A at $0.40\ \text{m/s}$.
(a) Calculate the water speed in sections B and C.
(b) Calculate the volume flow rate in each section.
(c) A student claims that because the water moves faster in C, more water passes through C each second than through A. Evaluate this claim.