2.2.3: Problems
- Page ID
- 32737
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Exercise \(\PageIndex{1}\): Blood flow through partially blocked artery
Blood flows in an artery with a partial blockage as shown in the animation (position is given in centimeters and time is given in seconds). Assume the blood can be treated as an ideal fluid. A blood platelet is shown moving through the artery. Which of the animations properly represents the motion of the platelet as it moves through and past the blockage? Explain. Restart.
Exercise \(\PageIndex{2}\): Density of liquid flowing through pipes
Assume an ideal fluid (position is given in meters and pressure is given in pascals). The dark brown in the animation represents a section of liquid as it flows into a region marked by the horizontal line and the corresponding water that must move out of the region in the top right. What is the density of the liquid? Restart.
Note
The format of the pressure is written in shorthand. For example, atmospheric pressure, \(1.01\times 10^{5}\text{ Pa}\), is written as \(1.01e+005\).
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{3}\): Water level in a leaky container
A wooden tank of water whose top is open to the atmosphere is shown (position is given in meters). Assume an ideal fluid. What is the water level in the tank? Restart.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{4}\): Pressure inside a leaky container
A tank of water is under pressure. What is the pressure at the top of the tank? Assume an ideal fluid (position is given in meters). Restart.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{5}\): Density of liquid in a leaky container
What is the density of the fluid in this reservoir? Assume an ideal fluid (position is given in meters and pressure is given in pascals). Restart.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{6}\): Liquid flowing through narrower pipes
Assume an ideal fluid (position is given in meters and pressure is given in pascals). The dark blue in the animation is a section of water (density \(1000\text{ kg/m}^{3}\)) as it flows through the pipes (assume they are cylindrical; that is, the vertical distances in the animation correspond to the diameter of the circular cross section). The pressure indicator can slide along the center of the pipes. Restart.
- What will the length of the dark blue region be in the narrowest tube?
- How fast will it go in the narrowest tube?
- What is the pressure in that tube?
Note
The format of the pressure is written in shorthand. For example, atmospheric pressure, \(1.01\times 10^{5}\text{ Pa}\), is written as \(1.01e+005\).
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{7}\): Identify the correct animation for liquid flowing through pipes
Which of the animations, if any, depicts a possible physical situation for ideal fluid flow? Explain what is wrong with the animations that are not physically possible. Assume an ideal fluid in each case (position is given in tenths of meters). The vertical tubes are open to the atmosphere. Assume all tubes are cylindrical. Restart.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{8}\): Boats in a flowing river
The animation shows an overhead view of two boats loosely moored to the banks of a river (position is given in meters). Restart.
- Explain why the boats move together as seen in the animation.
- If instead of a left-to-right flow of the river, the river water flowed from right to left, how would the animation change?
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{9}\): Water fountain pump
What is the gauge pressure of the pump of this water fountain in order for it to pump the water as shown? Treat the water as an ideal fluid. Assume the exit of the pump is where the water leaves the fountain (position is given in centimeters). The density of water is \(1000\text{ kg/m}^{3}\). Restart.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{10}\): Viscous flow
What is the viscosity of the fluid? The density of the fluid is \(900\text{ kg/m}^{3}\) (position is given in tenths of meters). The vertical tubes are open to the atmosphere. Assume the pipes are cylindrical. Restart.
Problem authored by Anne J. Cox.
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