Solving Fluid Statics Problem: Accounting for Atmospheric Pressure

[ChiralSuperfields]

Hi!

For this fluid statics problem,

One of the answers is:

However, why did they assume the pressure at the top was zero? I thought the pressure at the top would be 1 atm?

So tried to take atmospheric pressure into account putting 1 atm at the top,

Do you please know how to get P_0A/2 so that the P_0A/2 terms can cancel to get their hydrostatic force? I assume that the atmospheric pressure is the same at the top and bottom since the height of the dam is negligible to the scale of the atmosphere.

Many thanks!

 

[Baluncore]

However, why did they assume the pressure at the top was zero? I thought the pressure at the top would be 1 atm?

That one atmosphere is present above the water, through the water column, and also against the dry face of the dam wall. Those two atmospheric forces on the two sides of the dam wall oppose each other, and so can be cancelled.

 

[PeterDonis]

Moderator's note: Thread moved to introductory physics homework forum.

 

[haruspex]

How did you calculate P_avg?

 

[Orodruin]

That one atmosphere is present above the water, through the water column, and also against the dry face of the dam wall. Those two atmospheric forces on the two sides of the dam wall oppose each other, and so can be cancelled.

But the problem does not ask for the total net force on the dam. It asks for the resultant force exerted by the water on the dam. While the problem author likely intended to ask for the total net force, it is not what they wrote.

 

[ChiralSuperfields]

How did you calculate P_avg?

Thanks for your reply. I found P_avg by assuming the pressure at the top was 1 atm, and the pressure at the bottom was pgH then took the average (divided by 2). Many thanks,
Callum

 

[ChiralSuperfields]

That one atmosphere is present above the water, through the water column, and also against the dry face of the dam wall. Those two atmospheric forces on the two sides of the dam wall oppose each other, and so can be cancelled.

Thanks, yes, I agree. I just wanted to solve the problem by taking the atmosphere into account then cancelling with Newton's Second Law.

 

[Orodruin]

and the pressure at the bottom was pgH

Is it though?

 

[ChiralSuperfields]

Is it though?

Thanks for your reply, yeah true the pressure is p_0 + pgH which solves my confusion. Thank you very much for pointing that out!

 

[ChiralSuperfields]

But the problem does not ask for the total net force on the dam. It asks for the resultant force exerted by the water on the dam. While the problem author likely intended to ask for the total net force, it is not what they wrote.

Ok thank you for pointing that out!