7/25/2019 Fluid Mechanics 5th Year

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TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES – QUEZON CITY

Special Topics

Fluid Mechanics

A. Basic Properties of Fluids:a. Unit weightb. Densityc. Specific Volume

d. Specific Gravitye. Viscosityf. Surface Tension

1. Capillarity2. Pressure inside a droplet of liquid

B. Compression of Gasesa. Boyle’s Law b. Charles’ Law 

C. Pressuresa. Gage pressureb. Absolute pressure

D. Total Hydrostatic Pressurea. Total Pressure on Plane Surface:

=  b. Total Pressure on Curved Surface

E. Relative Equilibrium of Liquidsa. Horizontal Motion: =  

 

b. Inclined Motion: =   ±

 

c. Vertical Motion: = ( ± ) 

F. Rotation:

= 

 

=  = 

 

=   

1. A pressure gage 6m above the bottom of the tankcontaining a liquid reads 90 kPa, another gage height4m reads 103 kPa. Determine the specific weight ofthe liquid.

2. A two-meter square plane surface is immersedvertically below the water surface. The immersion issuch that the two edges of the square are horizontal.If the top of the square is 1 meter below the watersurface, what is the total water pressure exerted onthe plane surface?

3. An iceberg having specific gravity of 0.92 is floatingon salt water of sp. gr. 1.03. If the volume of ice abovethe 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 itimmersed in water and a force of 100N to keep itimmersed in glycerin (sp.gr.=13) find the weight andsp.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 tubediameter. 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 ischanged from 70kPa to 105kPa and the mercury levelin 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 of0.8m. The empty drum is submerged in water (with itstop 6m below the water surface), the air originallypresent in the drum remains composed there in at the

submerged depth. Find the height of air inside thedrum.

Situation:A gate 3.0m wide and 3.0m high has water on one side and isinclined at 45° with the horizontal. Water is 1.50m above thetop of the gate.

8. Compute the pressure (force) acting on the gate andits location from point A.

9. If the gate is hinged at the top, what force, appliedperpendicular to it, is needed at the bottom to justopen the gate?

10. In the figure shown, determine the horizontal andvertical components of the total force acting on thecylinder 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 isprovided with two steel hoops, one at the top and oneat the bottom. Compute the force in the bottom of thehoop.

12. A 5cm x 12cm x 6m long wooden plank is required tostand vertically in water with its top 15cm above thewater surface. This is attained by placing a 1.0cmthick steel plates to each wider side of the plank atthe 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, weighs4kN and 12kN, respectively. They are connected by ashort rope and placed in water. What is the tension inthe rope and what position will the lighter spherehave in relation with the water surface?

Situation:An open rectangular tank mounted on a truck is 5m long, 2mwide and 2.5m high is filled with water to a depth of 2m.

14. What maximum horizontal acceleration can beimposed 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 muchwater is spilled out?

Situation:An open cylindrical tank, 3m in diameter and 5m highcontains water to a depth of 4m. It is rotated about its ownvertical axis with a constant angular speed.

17. If angular velocity is 20rpm, is there any waterspilled?

18. What maximum value of ω (in rpm) can be imposedwithout spilling any liquid?

19. If angular velocity is 6 rad/sec, how much water isspilled out and to what depth will the water standwhen brought to rest?

20. What value of ω (rpm) will just zero the depth of waterat the center of the tank?