EK Physics #565

[Addallat]

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An open container of fluid (water is the fluid) begins drraining a spigot (assume ideal fluid flow).

H = height from spigot to top of container

Q585. If the container is filled with water, and H= 20 meters, the pressure at b is?
(b is at the midpoint of the container)

A. 1 atm
B. 2 atm
C. 3 atm
D. 4 atm

The answer is C. The explanation in the book states Pressure total = density(h)(g) + 1 atm

Can someone please explain

 

[JShen]

The formula for pressure at a point in a fluid is (density)(g)(h=depth). Since I'm assuming the tank is open to the atmosphere, you have atmospheric pressure also "pushing down" on the water, so you have to add atmospheric pressure (1 atm) to your calculation to get the total pressure at that point

 

[Addallat]

so if
g = 10 m/s^2
h = 20 m

I don't see where they're getting the density of water from. How is it that they're calulating the density of water as 1/100?

 

[reising1]

Since this is an open container, we have to add atmospheric pressure to our pressure equation:
P = pgh + Patm

As per the question, the fluid is filled with water. So we can update our equation
P = (p_water)(g)(h) + Patm

Now start filling in
P = (1000)(10)(20) + 10^5 = (10^3)(10)(2)(10) + 10^5 = (10^5)(2) + 10^5 = 3 * 10^5 Pascales = 3 atm

Some further notes of clarification
- when using P = pgh, the SI units are Pascals
- 1 atm is equal to 10^5 Pascals
- when using P = pgh, we must use the density of water (for the p term) in SI units, which is 1000 kg/m^3

 

[navho77]

An open container of fluid (water is the fluid) begins drraining a spigot (assume ideal fluid flow).

H = height from spigot to top of container

Q585. If the container is filled with water, and H= 20 meters, the pressure at b is?
(b is at the midpoint of the container)

A. 1 atm
B. 2 atm
C. 3 atm
D. 4 atm

The answer is C. The explanation in the book states Pressure total = density(h)(g) + 1 atm

Can someone please explain

What is meant by "b is the midpoint of the container"? Does it mean that b is at the same level as the spigot, in the center of the container?

 

[reising1]

point "b" is exactly "h" meters from the top of the water as is the spigot (I have EK and saw the picture)

 

[navho77]

point "b" is exactly "h" meters from the top of the water as is the spigot (I have EK and saw the picture)

All right, that all makes sense then.

 

[Addallat]

Some further notes of clarification
- when using P = pgh, the SI units are Pascals
- 1 atm is equal to 10^5 Pascals
- when using P = pgh, we must use the density of water (for the p term) in SI units, which is 1000 kg/m^3[/QUOTE]


ahhh thannks for clearing that up. I knew the density of water was 1000 kg/m^3

never realized 1 atmosphere =10^5 pascals <~~~ is this information that we'd be given in a passage or should i commit this to memory

so basically 1 atm = 10^5 pascals = 760 torr

 

[reising1]

never realized 1 atmosphere =10^5 pascals <~~~ is this information that we'd be given in a passage or should i commit this to memory

so basically 1 atm = 10^5 pascals = 760 torr

You should definitely commit this to memory. It might be given, but 75% chance not. A good solid review of SI units for all things in physics will be really useful to do, as some of the more obscure ones aren't intuitive (ex. power of a lens)