1) Calculate the pressure at the bottom of the Narragansett Bay, which is 56 m below sea level at its deepest point. A) 5.63094 × 10ª Pa B) 5.63094 × 105 Pa C) 5.63094 × 106 Pa D) 5.63094 × 10' Pa E) 5.63094 × 10® Pa F) 5.63094 x 10° Pa

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Chapter14: Fluid Mechanics
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Problem 10P: A tank with a flat bottom of area A and vertical sides is filled to a depth h with water. The...
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1) Calculate the pressure at the bottom of the Narragansett Bay, which is 56 m
below sea level at its deepest point.
A) 5.63094 × 10ª Pa
B) 5.63094 × 105 Pa
C) 5.63094 × 106 Pa
D) 5.63094 × 107 Pa
E) 5.63094 × 10 Pa
F) 5.63094 × 10° Pa
2) The pressure at the bottom of an average spot in the Narragansett Bay is only
about 7.800 x 10* Pa because most of the Bay is not as deep at its deepest spot.
Calculate the average depth below sea level. (The answer is a little surprising -
feel free to look this up if you want to check your result, but understand I
rounded the pressure quoted above so the correct answer doesn't agree exactly
with what you'll find)
A) 7.765 m
B) 10.61 m
C) 7.951 m
D) 7.757 m
E) 12.10 m
F) 7.959 m
3) The point on Earth farthest below sea level (that we know about) is under the
Pacific Ocean in the Mariana Trench at a depth of 11.034 km. Calculate the
pressure there.
A) 1.0813× 10® Pa
B) 1.0824 × 108 Pa
C) 5.6309 × 107 Pa
D) 1.0662 x 108 Pa
E) 1.1084 x 108 Pa
F) 1.1095 × 10° Pa
Transcribed Image Text:1) Calculate the pressure at the bottom of the Narragansett Bay, which is 56 m below sea level at its deepest point. A) 5.63094 × 10ª Pa B) 5.63094 × 105 Pa C) 5.63094 × 106 Pa D) 5.63094 × 107 Pa E) 5.63094 × 10 Pa F) 5.63094 × 10° Pa 2) The pressure at the bottom of an average spot in the Narragansett Bay is only about 7.800 x 10* Pa because most of the Bay is not as deep at its deepest spot. Calculate the average depth below sea level. (The answer is a little surprising - feel free to look this up if you want to check your result, but understand I rounded the pressure quoted above so the correct answer doesn't agree exactly with what you'll find) A) 7.765 m B) 10.61 m C) 7.951 m D) 7.757 m E) 12.10 m F) 7.959 m 3) The point on Earth farthest below sea level (that we know about) is under the Pacific Ocean in the Mariana Trench at a depth of 11.034 km. Calculate the pressure there. A) 1.0813× 10® Pa B) 1.0824 × 108 Pa C) 5.6309 × 107 Pa D) 1.0662 x 108 Pa E) 1.1084 x 108 Pa F) 1.1095 × 10° Pa
4) Some fish that evolved to live at extreme depths essentially explode if they are
Printed by Wolfram Mathematica Student Edition
2 | L07.02.nb
brought to the surface. This happens for the same reason that you would
essentially implode if you tried to go down to visit them without a very special
submarine. Let us approximate the cross sectional area of a fish (as viewed from
above) that might live in the Mariana Trench to be a rectangle of
2 cm x 10 cm = 20 cm² = 2 × 10-5 m³. Calculate the force this fish would feel
pushing down on it due to the ocean water above it.
A) 8 x 10° Pa
B) 8 x 1011 Pa
C) 6x 1012 Pa
D) 8 x 1014 Pa
E) 9 × 1011 Pa
F) 1× 1011 Pa
As an aside, even though this result is mind-boggling, the truth is even greater than this (for two rea-
sons)! To perform this calculation, we assume the gravitational acceleration is constantly 9.81 .
While this is a fine assumption most of the time, as we have seen in the course, the value of g actually
changes as you go farther from the surface of the Earth. At this depth its magnitude would be greater
than 9.81, so the pressure calculation underestimates the actual pressure. For the same reason, and
the fact that fluids aren't technically incompressible, the density increases a bit as you go deeper into
the ocean. Both these small errors in our approximations mean the pressure and thus the force here is
larger than what this calculation shows.
Transcribed Image Text:4) Some fish that evolved to live at extreme depths essentially explode if they are Printed by Wolfram Mathematica Student Edition 2 | L07.02.nb brought to the surface. This happens for the same reason that you would essentially implode if you tried to go down to visit them without a very special submarine. Let us approximate the cross sectional area of a fish (as viewed from above) that might live in the Mariana Trench to be a rectangle of 2 cm x 10 cm = 20 cm² = 2 × 10-5 m³. Calculate the force this fish would feel pushing down on it due to the ocean water above it. A) 8 x 10° Pa B) 8 x 1011 Pa C) 6x 1012 Pa D) 8 x 1014 Pa E) 9 × 1011 Pa F) 1× 1011 Pa As an aside, even though this result is mind-boggling, the truth is even greater than this (for two rea- sons)! To perform this calculation, we assume the gravitational acceleration is constantly 9.81 . While this is a fine assumption most of the time, as we have seen in the course, the value of g actually changes as you go farther from the surface of the Earth. At this depth its magnitude would be greater than 9.81, so the pressure calculation underestimates the actual pressure. For the same reason, and the fact that fluids aren't technically incompressible, the density increases a bit as you go deeper into the ocean. Both these small errors in our approximations mean the pressure and thus the force here is larger than what this calculation shows.
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