5

Ratio of pressure differenee across $1^{mathrm{st}}$ and $2^{mathrm{Dd}}$ ube when they are in serics is(a) $x$(b) $frac{x}{2}$(c) $frac{x}{8}$(d) $frac{x}{16}$...

Question

Ratio of pressure differenee across $1^{mathrm{st}}$ and $2^{mathrm{Dd}}$ ube when they are in serics is(a) $x$(b) $frac{x}{2}$(c) $frac{x}{8}$(d) $frac{x}{16}$

Ratio of pressure differenee across $1^{mathrm{st}}$ and $2^{mathrm{Dd}}$ ube when they are in serics is (a) $x$ (b) $frac{x}{2}$ (c) $frac{x}{8}$ (d) $frac{x}{16}$



Answers

At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 $ lb/in^2 $. Below the surface, the water pressure increases by 4.34 $ lb/in^2 $ for every 10 ft of descent.

(a) Express the water pressure as a function of the depth below the ocean surface.
(b) At what depth is the pressure 100 $ lb/in^2 $?

So if we want to write a function for the pressure, we know the pressure at the water level at the surface levels is 15 and increases by point for 34 for every foot of debt depth. So here's our function to find out when the pressure I went up to pressure the 100 we plug in 100 for the pressure 15 plus point for 34 x solve. For this, we have 85 equals 850.434 X x is 85 divided by 850.434 which is roughly 1 96 so that 1 96 feet about you get a pressure of 100 pounds per inch squared.

All right. In this problem, we're asked to convert blood pressure, which is usually expressed in millimetres of mercury to various other units. So first off, we need to know how these different units relate to one another and what their definitions are. So to start with one tour, one torch, Ellie is equal to one millimetre of mercury. That's the definition of a tour. Similarly, one Pascal is defined to be one Newtons per meter squared. And actually, I'm going to put another line right here said to know that this is actually the definition of a tour. And now, if we want to know how these different units relate to one another, it turns out that one tour is equal to 1.3 times 10 to the negative three atmospheres. And, um, this is also equal to 133 Paschal's. Now it's worth noting here that Paschal's air actually the scientific, the standard scientific units in the metric system and these other units, um, you're the millimeters mercury kind of arises for historical reasons through the use of barometers and expressing pressure in terms of multiples of the atmosphere can also be useful in certain settings, but it's worth remembering that the past scholars the is there say unit. So the blood pressure that appears in the numerator of a blood pressure reading the normal value for that is 122 millimeters of mercury and so straight from the definition of a tour. Um, this would be unchanged if we were to express the the units and tours. But if we want to express it in atmospheres, actually, let me just they could quick note of that. And if we want to express this in atmospheres, then we simply multiply 1 20 millimetres or 1 20 tour by the conversion factor for atmospheres. Two millimeters. Okay. And this will be equal toe 1 20 times, 133 our skulls, her millimeter and basically the conversions. They're going to be exactly the same for the denominator in the blood pressure reading, which is 80,000,000 years. So if we want to convert this to, um, units of atmospheres, all we do is we multiply a by 1.3 times 10 to the negative three. If we want to convert to pass calls, we multiply 80 by 133. And that's all

Okay, so the surface of the ocean, the water pressure is the same as the air pressure above the water, which is £15 per square inch below the surface. The water pressure will increase by £4.34 per square inch for every 10 ft of dissent. So we need to express the water pressure as a function of debt below the ocean surface. So since the water pressure is £15 per square inch when the depth of zero, the Y intercept is equal to £15 per square inch, and it says the water pressure increases by £4.34 per square inch for every 10 ft. That means the slope is zero point 434 Because we divide that number by 10 this is pound per square inch. This is a linear equation, so the water pressure P is equal to zero point 434 times the depth of the water plus 15. The true equation, Part B is at what depth is the pressure £100 per square inch. So we plug this into the equation and we're still working in units of pounds per square inch, so we don't have to do any converting their. So we have 100 is equal to zero point 434 times the depth plus 15. If we saw for the death, you will get 85 over 0.434 So this is equal to 195 0.9 the

Were given some data points about pressure at a certain depth of water. We were asked to derive a function of pressure as a function of death below the surface of the ocean, so were given. That's your pressure above the water, which is the surface of the ocean or a depth of zero feet, is £15 per swearing. So let's call X are get in feet below the surface of the ocean and let's call P of X, the pressure at depth sex below the surface. So we have that P A zero is equal to £15 per square inch, and we have that pressure increases by £4.34 per square inch for every 10 feet. So in particular for the 1st 10 feet of dissent, we have that the pressure is now the original pressure plus 4.34 pounds per square inch. This is equal to 15 plus 4.34 This is one way to do this. However, Another thing to see is that since we're assuming this is a Lanier, well, this is not assuming that were given. Slope is constant, so therefore, this is a one year function of X and cells he had X is equal to now her 10 feeds. We're changing by 4.34 Now that we look at this is by considering Slope as the difference in Why Difference and Ex So difference in why is 15 or Ph. Zero minus? He hit zero plus 4.34 over changing X, which is zero minus 10 is equal to 4.34 oh x plus be. This is equal to 4.3 4/10 or 0.434 X plus B, and we see that the value at zero is 15. So be People's 15 and therefore P of X is equal to 0.434 x plus. If team next were asked to find a depth such that there is a given pressure, any words? We were given a value of P X and rest to find X. Such that P of X is that value. So this is part B. We have that P Vex were saying it's going to be equal to £100 per square inch, therefore follows that this is equal to point 434 x plus 15 for some X we're gonna use algebra to solve for X. So this is equal to excuse me. This is equal to X is 100 minus 15 or 85 over 0.434 which is approximately equal to 196. Mrs. In feet. This is their answer for part B.


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