Imagine that the apparent weight of the crown in water is \(W_{\text {apparent }}=4.50 \mathrm{~N},\) and the actua weight is \(W_{\text {actual }}=5.00 \mathrm{~N}\). Is the crown made of pure \((100 \%)\) gold? The density of water is \(\rho_{\mathrm{w}}=1.00\) grams per cubic centimeter. The density of gold is \(\rho_{\mathrm{g}}=19.32\) grams per cubic centimeter.

- Yes
- No

In: Physics

Take the density of the crown to be \(\rho_{\mathrm{c}} .\) What is the ratio of the crown's apparent weight (in water) \(W_{\text {apparent }}\) to its actual weight \(W_{\text {actual }} ?\)

Express your answer in terms of the density of the crown \(\rho_{\mathrm{c}}\) and the density of water \(\rho_{\mathrm{w}}\)

\(\frac{W_{\text {apparent }}}{W_{\text {actual }}}=1-\frac{\rho_{w}}{\rho_{c}}\)

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Learning Goal: To understand the continuity equation.

Streamlines represent the path of the flow of a fluid. You can imagine that they represent a time-exposure photograph that shows the paths of small particles carried by the flowing fluid. The figure shows streamlines for the flow of an incompressible fluid in a tapered pipe of circular cross section. The speed of the fluid as it enters the pipe on the left is v_{1}. Assume that the cross-sectional areas of the pipe are A_{1} at its entrance on the left and A_{2} at its exit on the right.

Part A

Find F_{1}, the volume of fluid flowing into the pipe per unit of time. This quantity is also known as the volumetric flow rate.

Express the volumetric flow rate in terms of any of the quantities given in the problem introduction.

Part B

Because the fluid is assumed to be incompressible and mass is conserved, at a particular moment in time, the amount of fluid that flows into the pipe must equal the amount of fluid that flows out. This fact is embodied in the continuity equation. Using the continuity equation, find the velocity v_{2} of the fluid flowing out of the right end of the pipe.

Express your answer in terms of any of the quantities given in the problem introduction.

Part C

If you are shown a picture of streamlines in a flowing fluid, you can conclude that the __________ of the fluid is greater where the streamlines are closer together.

Enter a one-word answer.

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Arteriosclerotic plaques forming on the inner walls of arteries can decrease the effective cross-sectional area of an artery. Even small changes in the effective area of an artery can lead to very large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel.

Imagine a healthy artery, with blood flow velocity of v0=0.14m/s and mass per unit volume of ρ=1050kg/m3. The kinetic energy per unit volume of blood is given by K0=12ρv20.

Imagine that plaque has narrowed an artery to one-fifth of its normal cross-sectional area (an 80% blockage).

A) Compared to normal blood flow velocity, v0, what is the velocity of blood as it passes through this blockage? (Show your work)

B) By what factor does the kinetic energy per unit of blood volume change as the blood passes through this blockage?

C) As the blood passes through this blockage, what happens to the blood pressure?

1. It increases by about 41 Pa

2. It increases by about 250 Pa

3. It stays the same

4. It decreases by about 41 Pa

5. It decreases by about 250 Pa

D) Relative to its initial, healthy state, by what factor does the velocity of blood increase as the blood passes through this blockage?

E) By what factor does the kinetic energy per unit of blood volume increase as the blood passes through this blockage?

F) What is the magnitude of the drop in blood pressure, Δp, as the blood passes through this blockage? Use K0 as the normal (i.e., unblocked) kinetic energy per unit volume of the blood. (Show your work)

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Air flows through the tube shown in the figure. Assume that air is an ideal fluid.

What is the air speed v_{1} at point 1?

What is the air speed v_{2} at point 2?

What is the volume flow rate?

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It has been proposed that we could explore Mars using inflated balloons to hover just above the surface. The buoyancy of the atmosphere would keep the balloon aloft. The density of the Martian atmosphere is 0.0154 (although this varies with temperature). Suppose we construct these balloons of a thin but tough plastic having a density such that each square meter has a mass of 4.60 . We inflate them with a very light gas whose mass we can neglect. So far I found the following: What should be the radius of these balloons so they just hover above the surface of Mars? Radius of the balloon = /896 m What should be the mass of these balloons so they just hover above the surface of Mars? Mass of balloon = 4.64*10^-2 kg If we released one of the balloons from part A on earth, where the atmospheric density is 1.20 , what would be its initial acceleration assuming it was the same size as on Mars? If on Mars these balloons have five times the radius found in part A, how heavy an instrument package could they carry?

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At one point in a pipeline the water's speed is 3.00 m/s and the gauge pressure is 5.00 × 104 Pa. Find the gauge pressure at a second point in the line, 11.0 m lower than the first, if the pipe diameter at the second point is twice that at the first.

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A small circular hole 6.00 mm in diameter is cut in the side of a large water tank, 14.0 m below the tank's water level. The top of the tank is open to the air.

What is the speed of efflux?

What is the volume discharged per unit time?

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A spherical balloon has a radius of 6.95m and is filled with helium. The density of helium is 0.179 kg/m3, and the density of air is 1.29 kg/m3. The skin and structure of the balloon has a mass of 960kg. Neglect the buoyant force on the cargo volume itself. Determine the largest mass of cargo the balloon can lift.

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A hydraulic press for compacting powdered samples has a large cylinder which is 10.0 cm in diameter, and a small cylinder with a diameter of 2.0 cm. A lever is attached to the small cylinder as shown in (Figure 1). The sample, which is placed on the large cylinder, has an area of 4.0 cm2.

What is the pressure on the sample if F = 320N is applied to the lever?

Express your answer to two significant figures and include the appropriate units.

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A medical technician is trying to determine what percentage of a patient's artery is blocked by plaque. To do this, she measures the blood pressure just before the region of blockage and finds that itis 1.20×104 \(\rm Pa\), while in the region of blockage it is 1.15×104 \(rm Pa\). Furthermore, she knows that blood flowing through the normal artery just before the point of blockage is traveling at 30.0 \(rm cm/s\), and the specific gravity of this patient's blood is 1.06. What percentage of the cross-sectional area of the patient's artery is blocked by the plaque?

In: Physics

Water Flowing from a Tank

Water flows steadily from an open tank as shown in the figure. (Figure 1) The elevation of point 1 is \(10.0 \mathrm{~m},\) anc the elevation of points 2 and 3 is \(2.00 \mathrm{~m}\). The crosssectional area at point 2 is \(4.80 \times 10^{-2} \mathrm{~m}^{2} ;\) at point 3 where the water is discharged, it is \(1.60 \times 10^{-2} \mathrm{~m}^{2}\). The cross-sectional area of the tank is very large compared with the cross-sectional area of the pipe.

Part A

Assuming that Bernoulli's equation applies, compute the volume of water \(\Delta V\) that flows across the exit of the pipe in \(1.00 \mathrm{~s}\). In other words, find the discharge rate \(\Delta V / \Delta t\).

Express your answer numerically in cubic meters per second.

\(\frac{\Delta V}{\Delta t}= \mathrm{~m}^{3} / \mathrm{s}\)

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A pair of vertical, open-ended glass tubes inserted into a horizontal pipe are often used together to measure flow velocity in the pipe, a configuration called a Venturi meter. Consider such an arrangement with a horizontal pipe carrying fluid of density \(p\). The fluid rises to heights \({h_{1}}\) and \({h_{2}}\) in the two open-ended tubes (see figure). The cross-sectional area of the pipe is A1 at the position of tube 1, and \({A_{2}}\) at the position of tube 2.

Part A.Find \({p_{1}}\), the gauge pressure at the bottom of tube 1. (Gauge pressure is the pressure in excess of outside atmospheric pressure.)

Express your answer in terms of quantities given in the problem introduction and \({g}\), the magnitude of the acceleration due to gravity.

Part B.Find \({v_{1}}\), the speed of the fluid in the left end of the main pipe.

Express your answer in terms of \({h_{1}},{h_{2}}, g,\) and either \({A_{1}}\) and \({A_{2}}\) or \(\gamma\), which is equal to \(\frac{A_{1}}{A_{2}}\)

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What does the top pressure gauge in the figure read?

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A 1.0-cm-diameter pipe widens to 2.0 cm, then narrows to 0.5 cm. Liquid flows through the first segment at a speed of 4.0m/s.

A: What is the speed in the second segment?m/s

B: What is the speed in the third segment?m/s

C: What is the volume flow rate through the pipe?L/s

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