Fluid Mechanics 5th Year

TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES – QUEZON CITY Special Topics Fluid Mechanics A.

B.

C.

D.

E.

F.

Basic Properties of Fluids: a. Unit weight b. Density c. Specific Volume d. Specific Gravity e. Viscosity f. Surface Tension 1. Capillarity 2. Pressure inside a droplet of liquid Compression of Gases a. Boyle’s Law b. Charles’ Law Pressures a. Gage pressure b. Absolute pressure Total Hydrostatic Pressure a. Total Pressure on Plane Surface: 𝒅𝑭 = 𝜸𝒉𝒅𝑨 b. Total Pressure on Curved Surface Relative Equilibrium of Liquids 𝒂 a. Horizontal Motion: 𝒕𝒂𝒏 𝜽 = 𝒈 𝒂𝒉

b.

Inclined Motion: 𝒕𝒂𝒏 𝜽 =

c.

Vertical Motion: 𝝆 = 𝜸𝒉 (𝟏 ± )

Rotation:

𝒈±𝒂𝒗 𝒂

𝒈

𝝎𝟐 𝒙𝟐 𝟐𝒈 𝒅𝒚 𝝎𝟐 𝒙 𝒕𝒂𝒏 𝜽 = = 𝒅𝒙 𝒈 𝟏 𝟐 𝑽 = 𝝅𝒓 𝒉 𝟐 𝒚=

1. A pressure gage 6m above the bottom of the tank containing a liquid reads 90 kPa, another gage height 4m reads 103 kPa. Determine the specific weight of the liquid.

2. A two-meter square plane surface is immersed vertically below the water surface. The immersion is such that the two edges of the square are horizontal. If the top of the square is 1 meter below the water surface, what is the total water pressure exerted on the plane surface?

3. An iceberg having specific gravity of 0.92 is floating on salt water of sp. gr. 1.03. If the volume of ice above the water surface is 1000 cu.m., what is the volume of the ice?

4. A block of wood requires a force of 40 N to keep it immersed in water and a force of 100N to keep it immersed in glycerin (sp.gr.=13) find the weight and sp.gr. of the wood.

5. A capillary tube is immersed vertically in water. Knowing that water starts to evaporate below 2kPa, determine the maximum capillary rise and tube diameter. Assume the contact angle is 6 degrees and surface tension is 1 N/m.

6. The open manometer shown in the figure has for its gage liquid mercury. If the pressure at point m is changed from 70kPa to 105kPa and the mercury level in the sloping part moves 20cm upward to the right, what could have been the value of θ?

7. An empty drum has a height of 3m and a radius of 0.8m. The empty drum is submerged in water (with its top 6m below the water surface), the air originally present in the drum remains composed there in at the

submerged depth. Find the height of air inside the drum. Situation: A gate 3.0m wide and 3.0m high has water on one side and is inclined at 45° with the horizontal. Water is 1.50m above the top of the gate. 8. Compute the pressure (force) acting on the gate and its location from point A. 9. If the gate is hinged at the top, what force, applied perpendicular to it, is needed at the bottom to just open the gate?

10. In the figure shown, determine the horizontal and vertical components of the total force acting on the cylinder per m of its length/

11. A wooden storage vat full of oil (s.g. = 0.80) is in the form of a frustum of a cone, 2m diameter at the top, 4m diameter at the bottom and 3m height. It is provided with two steel hoops, one at the top and one at the bottom. Compute the force in the bottom of the hoop.

12. A 5cm x 12cm x 6m long wooden plank is required to stand vertically in water with its top 15cm above the water surface. This is attained by placing a 1.0cm thick steel plates to each wider side of the plank at the submerged bottom. The specific weights are: Wood = 502 kg/m3 Steel = 7870 kg/m3 Compute the exact length of steel plates needed.

13. Two spheres, both to have a diameter of 1.2m, weighs 4kN and 12kN, respectively. They are connected by a short rope and placed in water. What is the tension in the rope and what position will the lighter sphere have in relation with the water surface? Situation: An open rectangular tank mounted on a truck is 5m long, 2m wide and 2.5m high is filled with water to a depth of 2m. 14. What maximum horizontal acceleration can be imposed on the tank without spilling any water? 15. Determine the accelerating force on the liquid mass. 16. If the acceleration is increased to 6m/s2, how much water is spilled out? Situation: An open cylindrical tank, 3m in diameter and 5m high contains water to a depth of 4m. It is rotated about its own vertical axis with a constant angular speed. 17. If angular velocity is 20rpm, is there any water spilled? 18. What maximum value of ω (in rpm) can be imposed without spilling any liquid? 19. If angular velocity is 6 rad/sec, how much water is spilled out and to what depth will the water stand when brought to rest? 20. What value of ω (rpm) will just zero the depth of water at the center of the tank?