Fluid Dynamics - Hydrostatic Pressure

In summary: The pressure at the top of the plate is 0.6 m below the surface of the water, and the pressure at the bottom of the plate is 1.2 m below the surface of the water. The hydrostatic force on the vertical plate is the integral of the pressure with respect to the area of the plate, and this force varies with depth. The problem is asking for the depth where a horizontal line can be drawn on the plate such that the hydrostatic forces on either side of the line are equal. This depth can be found by setting the integral of the pressure on one side of the line equal to the integral of the pressure on the other side of the line and solving for depth. The answer is
  • #1
Lukas_RSA
6
0

Homework Statement


A rectangular vertical plate is submerged in water. The top edge is horizontal and at a depth of 0.6m. The length of the vertical edge is 1.2m. determine at what dept under the water surface a horizontal line can be drawn on the plate such that the hydrostatic forces on either side of the line is equal. (Hint: The magnitude of the hydrostatic force on a vertical surface is equal to the average pressure x the area.)
!answer: 1.342m

Homework Equations

The Attempt at a Solution



l1 = 2/3 x 'h
l1 = 2/3 x 1.8
l1 = 1.2

i am not even sure how to draw this question, there is no picture with the question, normally i start off by drawing the problem and adding all the know values,

please help me with this problem.

i hope to hear from you soon.

regards
Lukas van Rooyen
 
Physics news on Phys.org
  • #2
Lukas_RSA said:

Homework Statement


A rectangular vertical plate is submerged in water. The top edge is horizontal and at a depth of 0.6m. The length of the vertical edge is 1.2m. determine at what dept under the water surface a horizontal line can be drawn on the plate such that the hydrostatic forces on either side of the line is equal. (Hint: The magnitude of the hydrostatic force on a vertical surface is equal to the average pressure x the area.)
!answer: 1.342m

Homework Equations

The Attempt at a Solution



l1 = 2/3 x 'h
l1 = 2/3 x 1.8
l1 = 1.2

i am not even sure how to draw this question, there is no picture with the question, normally i start off by drawing the problem and adding all the know values,

please help me with this problem.

i hope to hear from you soon.

regards
Lukas van Rooyen
Well, take it in steps.

1. A rectangular plate is submerged in water.
The surface of the water is located above the top edge of the plate.

2. This plate is vertical.
This means the plate is oriented such that its height is perpendicular to the surface of the water, while its width is parallel to the surface of the water.

3. The length of the vertical edge is 1.2 m.
This plate is 1.2 m tall in the vertical direction, perpendicular to the surface of the water.

4. The top edge is horizontal and at a depth of 0.6 m.
This means the top edge of the plate is 0.6 m below the surface of the water. The top edge is also parallel with the surface of the water.

You should be able to make a sketch of the plate using these four characteristics.

Determine at what depth under the water surface a horizontal line can be drawn on the plate such that the hydrostatic forces on either side of the line are equal. (Hint: The magnitude of the hydrostatic force on a vertical surface is equal to the average pressure x the area.)
!answer: 1.342 m

You should make a sketch which shows how hydrostatic pressure varies with depth along the vertical edge of the submerged plate.
 

1. What is fluid dynamics?

Fluid dynamics is the study of how fluids (liquids and gases) behave when they are in motion. This includes understanding the forces and pressures that affect the movement of fluids.

2. What is hydrostatic pressure?

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above it. It is directly proportional to the density of the fluid and the depth of the fluid.

3. How is hydrostatic pressure calculated?

Hydrostatic pressure can be calculated using the formula P = ρgh, where P is the hydrostatic pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid.

4. How does hydrostatic pressure affect objects in a fluid?

Objects in a fluid are subject to hydrostatic pressure from all directions. The pressure increases with depth, so objects deeper in the fluid will experience greater pressure. This can cause objects to sink or float depending on their density.

5. What are some real-world applications of hydrostatic pressure?

Hydrostatic pressure is used in many industries, such as in hydraulic systems, water transportation, and scuba diving. It also plays a crucial role in natural phenomena, such as the circulation of ocean currents and the movement of groundwater.

Similar threads

B What actually is static pressure?
    • Thermodynamics
Replies
11
Views
262
Fluid Mechanics Challenging Problem
    • Introductory Physics Homework Help
Replies
10
Views
1K
Hydrostatic pressure in a tilted tube
    • Introductory Physics Homework Help
Replies
6
Views
2K
I A specific case of an exception to Archimedes' Principle?
    • Mechanics
2
Replies
40
Views
2K
Pressure on a vertical rectangular plate submerged in water
    • Introductory Physics Homework Help
Replies
15
Views
2K
Fluid Dynamics - Hydrostatic Pressure #2
    • Introductory Physics Homework Help
Replies
4
Views
1K
Engineering Hydrodynamic force on hinged flap gate
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Question about hydrostatic pressures
    • Introductory Physics Homework Help
Replies
10
Views
2K
Calculating hydrostatic force & locating centre of pressure
    • Introductory Physics Homework Help
Replies
5
Views
9K
Basics of hydrostatic force on a plane surface
    • Introductory Physics Homework Help
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top