PP 9.3-9.4_1

# PP 9.3-9.4_1 - Applications Physics of Hydrostatic Pressure...

This preview shows pages 1–10. Sign up to view the full content.

Applications

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Physics of Hydrostatic Pressure and Force A thin horizontal plate of area A m 2 is submerged in a fluid of density ρ kg/m 3 , at a depth of d m below the surface.
The pressure P on the plate is defined to be the force per unit square: The cylinder of fluid directly above the plate has volume V = Ad , so its mass is m = ρV = ρAd . Hence the force exerted on the plate by the fluid is: gAd mg F ρ = = where g is the acceleration due to gravity gd A F P = =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The Principle of Direction Invariance At any point in a liquid the pressure is the same in all directions . Thus the pressure in all directions at a depth d in a fluid of density ρ is gd P ρ =
Example A dam has the shape of a trapezoid. The height is 20m, the width is 50m at the top, and 30m at the bottom. The water level is 4m below the top of the dam. Find the force on the dam due to hydrostatic pressure.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The difficulty here is that the pressure on the dam increases with depth. So we need to accumulate together the forces on the dam wall at each depth. Fix a vertical x -axis, with the origin at the surface of the water. The water depth is 16m.
Approximate the pressure on the dam as follows: Divide [0 , 16] into equal subintervals, each of length Δ x = 16 /n Pick points x i * in successive subintervals The i th approximating rectangle has height Δ x , width w i and area A i = w i Δ x .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Using similar triangles w i = 46 - x i * .
For small x , the pressure on the i th rectangle, P i , is almost constant, so P i 1000 gx i * Hence the hydrostatic force,

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 01/21/2011 for the course PHYS 4A 60865 taught by Professor L. oldewurtel during the Fall '09 term at Irvine Valley College.

### Page1 / 26

PP 9.3-9.4_1 - Applications Physics of Hydrostatic Pressure...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online