Horizontal force on one side

[jbowers9]

A square tank 12 feet high having a perimeter of 40 feet is filled with water weighing 62.4 pounds per cubic foot. The total horizontal force on one side of the tank due to the water pressure is MOST NEARLY ________ pounds.

A. 58,000
B. 45,000
C. 36,000
D. 13,000

The answer key says 45,000 lbs. is the answer but I have no clue how they got there.
Total pressure - lbs./ft^2 - should be 12 x 62.4, or 5.2lbs/in^2. How do they get 45,000?

 

[CompuChip]

First: what is the volume of the tank? Note that 40 feet is the perimeter. Secondly, how do you calculate the horizontal force given the volume of water and the weight (look in your textbook or lecture notes)

 

[jbowers9]

Square Tank

with perimeter 40 feet. So each side is 10 feet. I really am mildly ashamed to admit that I don't recall a formula for "horizontal" pressure. I thought pressure at the same depth was the same throughout a fluid. This question is for a State Civile Service exam. NY State. Maybe we do things differently.

 

[tiny-tim]

with perimeter 40 feet. So each side is 10 feet. I really am mildly ashamed to admit that I don't recall a formula for "horizontal" pressure. I thought pressure at the same depth was the same throughout a fluid. This question is for a State Civile Service exam. NY State. Maybe we do things differently.

Hi jbowers9!

Yes, pressure is the same in all directions at any fixed height.

Hint: force = pressure times area.

And how does the pressure change with the depth?

 

[jbowers9]

Horizontal Pressure

OK

So the area of the tank is 100ft^2...
It's 12 ft high...
62.4 x 10 X 10 X 12 gives total force which is not 45,000 lbs.

 

[tiny-tim]

OK

So the area of the tank is 100ft^2...
It's 12 ft high...
62.4 x 10 X 10 X 12 gives total force which is not 45,000 lbs.

urgh! :yuck:

That's the mass!

HINT:

how does the pressure change with the depth?

 

[jbowers9]

Horizontal "Force"

Actually, the density x volume IS the force in the English system. Lbs. is a measure of force (mass x g). The English system of mass is the slug.
I figured it out Saturday evening. 62.4y - if y is the verticle coordinate - is the PRESSURE at any depth y in the tank (lbs/ft^2). 10dy is an element of area along one side of the tank.
642 y dy integrated over the limits 0 - 12 give 642 x 72 = 46,224 which is close enough to the given answer of 45,000 for me. Notice that the dimension of the answer is pounds. Which is a unit of FORCE in the English system. Thank you.

 

[tiny-tim]

Hi jbowers9!

Actually, the density x volume IS the force in the English system. Lbs. is a measure of force (mass x g). The English system of mass is the slug.

I did know that!

But the mass (in pounds) is a vertical force, and you were asked for the horizontal force!

I figured it out Saturday evening. 62.4y - if y is the verticle coordinate - is the PRESSURE at any depth y in the tank (lbs/ft^2). 10dy is an element of area along one side of the tank.
642 y dy integrated over the limits 0 - 12 give 642 x 72 = 46,224 which is close enough to the given answer of 45,000 for me. Notice that the dimension of the answer is pounds. Which is a unit of FORCE in the English system. Thank you.

erm … I think you'd get a lot closer if you used 624 instead of 642.