where A is the cross-sectional area and [latex]\barv\\[/latex] is the average velocity. This equation seems logical enough. The relationship tells us that flow rate is directly proportional to both the magnitude of the average velocity (hereafter referred to as the speed) and the size of a river, pipe, or other conduit. The larger the conduit, the greater its cross-sectional area. Figure 1 illustrates how this relationship is obtained. The shaded cylinder has a volume
We note that Q=V/t and the average speed is [latex]\overlinev=d/t\\[/latex]. Thus the equation becomes [latex]Q=A\overlinev\\[/latex]. Figure 2 shows an incompressible fluid flowing along a pipe of decreasing radius. Because the fluid is incompressible, the same amount of fluid must flow past any point in the tube in a given time to ensure continuity of flow. In this case, because the cross-sectional area of the pipe decreases, the velocity must necessarily increase. This logic can be extended to say that the flow rate must be the same at all points along the pipe. In particular, for points 1 and 2,
A nozzle with a radius of 0.250 cm is attached to a garden hose with a radius of 0.900 cm. The flow rate through hose and nozzle is 0.500 L/s. Calculate the speed of the water (a) in the hose and (b) in the nozzle.
We could repeat this calculation to find the speed in the nozzle [latex]\barv_2\\[/latex], but we will use the equation of continuity to give a somewhat different insight. Using the equation which states
The solution to the last part of the example shows that speed is inversely proportional to the square of the radius of the tube, making for large effects when radius varies. We can blow out a candle at quite a distance, for example, by pursing our lips, whereas blowing on a candle with our mouth wide open is quite ineffective. In many situations, including in the cardiovascular system, branching of the flow occurs. The blood is pumped from the heart into arteries that subdivide into smaller arteries (arterioles) which branch into very fine vessels called capillaries. In this situation, continuity of flow is maintained but it is the sum of the flow rates in each of the branches in any portion along the tube that is maintained. The equation of continuity in a more general form becomes
The aorta is the principal blood vessel through which blood leaves the heart in order to circulate around the body. (a) Calculate the average speed of the blood in the aorta if the flow rate is 5.0 L/min. The aorta has a radius of 10 mm. (b) Blood also flows through smaller blood vessels known as capillaries. When the rate of blood flow in the aorta is 5.0 L/min, the speed of blood in the capillaries is about 0.33 mm/s. Given that the average diameter of a capillary is 8.0 μm, calculate the number of capillaries in the blood circulatory system.
We can use [latex]Q=A\overlinev\\[/latex] to calculate the speed of flow in the aorta and then use the general form of the equation of continuity to calculate the number of capillaries as all of the other variables are known.
Note that the speed of flow in the capillaries is considerably reduced relative to the speed in the aorta due to the significant increase in the total cross-sectional area at the capillaries. This low speed is to allow sufficient time for effective exchange to occur although it is equally important for the flow not to become stationary in order to avoid the possibility of clotting. Does this large number of capillaries in the body seem reasonable? In active muscle, one finds about 200 capillaries per mm3, or about 200 106 per 1 kg of muscle. For 20 kg of muscle, this amounts to about 4 109 capillaries.
2. Many figures in the text show streamlines. Explain why fluid velocity is greatest where streamlines are closest together. (Hint: Consider the relationship between fluid velocity and the cross-sectional area through which it flows.)
6. A major artery with a cross-sectional area of 1.00 cm2 branches into 18 smaller arteries, each with an average cross-sectional area of 0.400 cm2. By what factor is the average velocity of the blood reduced when it passes into these branches?
7. (a) As blood passes through the capillary bed in an organ, the capillaries join to form venules (small veins). If the blood speed increases by a factor of 4.00 and the total cross-sectional area of the venules is 10.0 cm2, what is the total cross-sectional area of the capillaries feeding these venules? (b) How many capillaries are involved if their average diameter is 10.0 μm?
8. The human circulation system has approximately 1 109 capillary vessels. Each vessel has a diameter of about 8 μm. Assuming cardiac output is 5 L/min, determine the average velocity of blood flow through each capillary vessel.
10. The flow rate of blood through a 2.00 10-6-radius capillary is 3.80 109. (a) What is the speed of the blood flow? (This small speed allows time for diffusion of materials to and from the blood.) (b) Assuming all the blood in the body passes through capillaries, how many of them must there be to carry a total flow of 90.0 cm3/s? (The large number obtained is an overestimate, but it is still reasonable.)
11. (a) What is the fluid speed in a fire hose with a 9.00-cm diameter carrying 80.0 L of water per second? (b) What is the flow rate in cubic meters per second? (c) Would your answers be different if salt water replaced the fresh water in the fire hose?
14. Prove that the speed of an incompressible fluid through a constriction, such as in a Venturi tube, increases by a factor equal to the square of the factor by which the diameter decreases. (The converse applies for flow out of a constriction into a larger-diameter region.)
15. Water emerges straight down from a faucet with a 1.80-cm diameter at a speed of 0.500 m/s. (Because of the construction of the faucet, there is no variation in speed across the stream.) (a) What is the flow rate in cm3/s? (b) What is the diameter of the stream 0.200 m below the faucet? Neglect any effects due to surface tension.
16. Unreasonable Results A mountain stream is 10.0 m wide and averages 2.00 m in depth. During the spring runoff, the flow in the stream reaches 100,000 m3/s. (a) What is the average velocity of the stream under these conditions? (b) What is unreasonable about this velocity? (c) What is unreasonable or inconsistent about the premises?
Internet speeds have been on a steady incline for years, and speeds really ramped up since the onset of the COVID-19 pandemic in 2020. Internet providers have diversified plan options and ramped up efforts to expand fiber-optic networks, making it possible to now offer plans capable of eye-popping max speeds: 1Gbps, 2Gbps, and even 5Gbps.
The disparity between the two figures suggests that the majority of internet users still order relatively modest internet packages with speeds of 200Mbps or below, usually due to factors like price and availability.
As was the case last year, states along the Eastern Seaboard continue to lead in internet speed. Seven of the top 10 fastest states this year are located in New England or the New York Tri-State area. Two of the states (Florida and South Carolina) are also on the East Coast, just farther south.
Connecticut gets average download speeds of just over 194Mbps and median speeds of 119.13Mbps. New Jersey gets a faster average download speed (202.2Mbps) but a slightly slower median speed (118.57Mbps). Florida comes in close behind with 185.24Mbps average speeds and 115.58Mbps median speeds.
Why so fast? Connecticut, New Jersey, Florida, and Delaware are some of the most densely populated states in the country, which vastly improves their chances for getting top-quality internet service. Internet providers tend to prioritize areas with a lot of customers to justify the cost of expanding network access and offering competitive deals.
Advertised download speeds up to 2048Mbps Connection types: Fiber and 5G Home Check Availability Zip code Page 1 Created with Sketch. _Custom/UI/ic_placeholder View Plans Fastest speeds in New Jersey
Advertised download speeds up to 2,048Mbps Connection types: Fiber and 5G Home Check Availability Zip code Page 1 Created with Sketch. _Custom/UI/ic_placeholder View Plans Fastest speeds in Florida
Alaska, West Virginia, and Kansas also saw massive improvements in internet speed last year. Considering that Alaska and West Virginia also rank first and second for the slowest speeds in America, respectively, these improvements suggest that Wi-Fi may be slowly but surely getting better for everyone.
The Federal Communications Commission has pledged to increase access to affordable, high-speed internet options, with a goal of first boosting minimum speed standards and eventually providing 100% internet access nationwide. The government can focus its energies on these states first.
I have no idea how much traffic is on the road or how fast they drive though. It does seem like there are pull outs pretty frequently if traffic starts to back up behind me. I thought maybe people wouldn't be going as fast as they seem to do everywhere else in the country (where going the speed limit seems to be a minimum, not a maximum) as they'd also be trying to appreciate the view. Plus in all my google streetviewing, I didn't see any speed limit signs except one before a curve.
State law says that if five or more vehicles are following you on a rural highway, you must pull over at the next turnout and let them pass. The problem is that there are many tourists and inexperienced drivers who fail to obey the law, then they end up creeping along rural highways below the speed limit for long periods of time and disrupting the travel plans of all the drivers stuck behind them. So you need to be prepared for that scenario.
Let's go back a step... how long do you have for this drive (and I really hope the answer is 2 or more nights)? You generally want to spend 1 night in the (ta && ta.queueForLoad ? ta.queueForLoad : function(f, g)document.addEventListener('DOMContentLoaded', f);)(function()ta.trackEventOnPage('postLinkInline', 'impression', 'postLinks-78833902', '');, 'log_autolink_impression');Monterey area and the second in the Pismo Beach area. The drive between the two will be the slowest portion, with average speeds may 35-40 mph. I'm usually one of those drivers going at or below the speed limit, so I pull over constantly. But be aware that the pull-outs may be simply a wide dirt shoulder next to a steep cliff (although state law says you can wait for a paved area to pull over).
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