The vertical surface of a reservoir dam that is in contact with the water is 120 m wide and 12 m high. The air pressure is one atmosphere. Find the magnitude of the total force acting on this surface in a completely filled reservoir.
Question
The vertical surface of a reservoir dam that is in contact with the water is 120 m wide and 12 m high. The air pressure is one atmosphere. Find the magnitude of the total force acting on this surface in a completely filled reservoir.
Solution
To solve this problem, we need to use the formula for pressure at a depth in a fluid, which is P = ρgh, where ρ is the density of the fluid (in this case, water), g is the acceleration due to gravity, and h is the height of the fluid above the point in question.
Step 1: Identify the knowns
- The density of water, ρ, is typically 1000 kg/m³.
- The acceleration due to gravity, g, is approximately 9.8 m/s².
- The height of the water, h, is 12 m.
- The width of the dam, w, is 120 m.
Step 2: Calculate the pressure at the bottom of the dam Using the formula P = ρgh, we find that the pressure at the bottom of the dam is P = (1000 kg/m³)(9.8 m/s²)(12 m) = 117,600 Pa (Pascal).
Step 3: Calculate the force on the dam The force on the dam is given by the pressure times the area over which it acts. The area of the dam is its width times its height, or A = wh = (120 m)(12 m) = 1440 m². Therefore, the force on the dam is F = PA = (117,600 Pa)(1440 m²) = 169,344,000 N.
So, the magnitude of the total force acting on the surface of the dam in a completely filled reservoir is 169,344,000 N.
Similar Questions
A flat surface with the shape of an equilateral triangle is submerged in water so that its flat surface is perpendicular to the free surface and one leg is just below the free surface as shown in Figure. Length of a leg of the equilateral triangle is 2.10 m. Calculate the magnitude of the pressure force acting on the surface.
A container has a large cylindrical lower part with a long thin cylindrical neck. The lower part of the container holds 12.5 m3 of water and the surface area of the bottom of the container is 5.00 m2. The height of the lower part of the container is 2.50 m and the neck contains a column of water 8.50 m high. The total volume of the column of water in the neck is 0.200 m3. What is the magnitude of the force exerted by the water on the bottom of the container?
5. Water is filled in a flask upto a height of 20 cm. The bottom of the flask is circular with radius 10 cm. If the atmospheric pressure is 1.013 × 105 Pa, find the force exerted by the water on the bottom. Take 8 = 10 ms and density of water = 1000 kgm™³.
What is the total force on the bottom of a 2.0-m-diameter by 2.0-m-deep round wading pool due to the weight of the air and the weight of the water? (Note the pressure contribution from the atmosphere is 1.0 × 105 N/m2, the density of water is 1 000 kg/m3, and g = 9.8 m/s2.)Select one:a.2.3 × 105 Nb.5.3 × 106 Nc.3.8 × 105 Nd.15 × 106 Ne.3.8 × 106 N
A flat rectangular plate, dimension 1.5m length by 0:5m width is immersed in saline waterdensity 1025kg/m) such that their greatest and least depths are 1:80m and 0.80mrespectively. Determine the force exerted on one face by the water pressure.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.