MECHANICAL: July 2012

1. A jet of water of 100 mm diameter impinges normally on a fixed plate with a velocity of 30 m/s. Find the force exerted on the plate.

2. A jet of water of 100 mm diameter, moving with a velocity of 20 m/s strikes a stationary plate. Find the force on the plane in the direction of the jet, when

(a) The plate is normal to the jet

(b) The angle between the jet and plate is 45 deg

3. A jet of water of 50 mm diameter, moving with a velocity of 26 m/s is impinging normally on a plate. Determine the pressure on the plat, when (a) it is fixed and (b) it is moving with a velocity of 10 m/s in the direction of the jet

4. A jet of water diameter 60 mm moving with a velocity of 40 m/sec strikes a curved fixed plate tan at one end at an angle of 30 deg to horizontal, the jet leaves the plate at an angle 20 deg to the horizontal. Find the force exerted by the jet on the plate in the horizontal and vertical direction.

5. A jet of water 80 mm in diameter moving with a velocity of 60 m/sec strikes a fixed center of curved plate, if the jet deflected to an angle 130 deg , determine the forces

6. A jet of water strikes a velocity of 35 m/sec on a flat plate inclined at 30 deg with the axis of jet if the cross section area of the jet is 25 cm2, determine: force exerted by the jet on plate the component of the force in the direction of the jet

7. A jet of water of 12 mm diameter impinges normally at the center of a fixed vane which deflects jet at 165 deg, if the reaction of vane was found to be 35 N, when the discharge on the jet was 225 kg in 150 second. Find the ratio of 1) actual to theoretical force of jet 2) outlet velocity to the inlet velocity

8. A jet of the water strikes to the fixed curved plate tangentially with velocity of 27.5 m/sec and leaves the jet through 60 deg, if the discharge through nozzle = 1025 gm/sec calculate the magnitude and direction of the resultant force.

9. A water jet radius 75 mm moving with the velocity 15 m / sec and strikes to the curved plate at the center, find force exerted by the jet of water in the direction of the jet if the jet is deflected through an angle of 120 deg at the outlet of the curved plate.

1. A reservoir of glycerin has a mass of 1200 kg and a volume of 0.952 m3. Find the glycerin weigh W, mass density, sp weight and sp gravity.

2. A body requires a force of 100 N to accelerate it at a rate of 0.20 m/sec2 determine the mass of the body in Kg

3. A reservoir of carbon tetra chloride has a mass of 500 Kg, and a volume of 0.315 m3. Find the carbon tetra chloride’s weight, mass density, sp weigh and sp gravity.

4. The volume of a rock is found to be 0.00015 m3. If the rock’s sp gravity is 2.60, what is its weigh?

5. If the sp weight of the substance is 8.2 kN/m3, what is its mass density?

6. Find the height of the free surface if 0.8 m3 of water is poured into a conical tank (Fig 1) 20 in height with a base rad. of 10 m . How much additional water is required to fill the tank?

7. In above example, if the tank holds 30.5 Kg of Oil, what is the density of the oil?

8. A liquid compressed in a cylinder has a volume of 1000 cm3 at 1 MN/m2 and a volume of 995 cm3 at 2 MN/m2. What is its bulk modulus of elasticity?

9. Find the bulk modulus of elasticity of a liquid if a pressure of 10.35 bar, applied to 0.258 m3 of the liquid causes the volume reduction of 0.000566 m3

10. If modulus of elasticity of water is 2.2 GPa, What Pressure is required to reduce the volume by 0.6%?

11. Find the change in volume of 0.0283 m3 of water at 80 F when subjected to pressure increase of 20.7 bar. Water’s bulk modulus of elasticity of temp is 22425 bar

12. From the following test data , determine the bulk modulus of elasticity of water at 34.5 bar the volume was 28317 cm3, and at 241.5 , the volume was 2803 cm3

13. Water in a hydraulic press, initially at 1.38 bar, is subjected to a pressure of 1173 bar at 68 F (temp) , determine the % decrease in sp volume. The avg bulk modulus of elasticity is 25185 bar.

14. At a depth of 7 km in the ocean, the pressure is 71.6 Mpa assume of sp weight at the surface of 10.05 KN/m3 and an avg bulk modulus of elasticity of 2.34 GPa for that pressure range. Find a) the change in sp volume between the surface and 7 KN b) the specific volume at 7 Km c) Sp weight at 7 Km

15. What is the sp weight of air at the temp of 30c and pressure of 470 KPa(abs).

16. A large plate moves with speed V0 over a stationary plate on a layer of oil, (Fig 2). If the velocity profile is that of a parabola, with the oil at the plates having the same velocity as the plates, what is the shear stress on the moving plate from the oil? If a linier profile is assume, what is the shear stress on the plate?

17. A square block weighing 1.1 KN and 250 mm on an edge slides down an incline on a film of oil 6.0µm thick, see fig 3. Assuming the linier velocity profile in the oil, what is the terminal speed of the block? The viscosity of the oil is 7 mPa.s

18. A piston of weight 10 Kg slides in a lubricated pipe, as shown in fig 4. The clearance between piston and pipe is 0.001 inch. If the piston decelerates at 2.1 ft/sec2 when the speed is 21 ft/sec, what is the viscosity of oil?

19. Benzene at 20 c has a viscosity of 0 .00651 Pa.sec. what shear stress is require to deform this fluid at a strain rate of 4900 (1/sec)

20. A shaft 70 mm in diameter is being push at speed of 400 mm/sec through s bearing sleeve 70.2 mm in diameter. And 250 mm long. The clearance, assume uniform, is lifted with oil at a 20 c with kinematic viscosity = 0.05 m2/sec and sp gravity= 0.9. Find the force exerted by the oil on the shaft.

21. A disc of rad R1 rotates at angular velocity v inside an oil bath of viscosity µ , as shown in fig 5 . Assuming a linier velocity profile and neglecting shear on the outer disc edges, derive an expression for the viscous torque on the disc.

22. Determine the viscosity of fluid between shaft and sleeve in fig 6.

23. A glass tube is inserted in mercury (fig 7) the common temp is 20 c . What is the upward force on the glass as a result of surface effect?

24. Find the capillary rise in the tube shown in fig 8 for a water-air-glass interface (U=0 deg) if the tube rad is 1 mm and the temp is 20 c.

25. The surface tension of mercury and water at 60 c are 0.47 N/m and 0.0662 N/m , respectively. What capillary height changes will occur in these two fluids when they are in contact with air in a glass tube of rad 0.30? Use U=130 deg for mercury, and 0 deg for water: sp weight 132.3 KN/m3 for mercury and 9.650 KN/m3 for water.

26. At 30 c what diameter glass tube is necessary to keep the capillary height change of water less than 2 mm?

27. The glass tube in fig 9 is used to measure pressure P1 in water tank. The tube diameter is 1 mm and the water is at 30 c. After correcting for a surface tension what is the true water height in the water tube.

28. For the dam shown in fig 9, find the horizontal pressure acting at the face of the dam at 20 ft depth.

29. For the vessel containing glycerin under pressure as shown in fig 10 find the pressure at the bottom of the tank

30. The weather report indicates the barometric pressure is 29.75 inch of mercury. What is the atm pressure?

31. Find the atm pressure in KPa if a mercury barometer reads 742mm.

32. A pressure gauge 7.0 above the bottom of the tank containing a liquid reads 64.94 KPa another gauge at height 4.0 m reads 87.53 KPa. Compute the sp weight and mass density of fluid.

33. An open tank contain 5.7 m of water covered with 2.58 m of kerosene, (sp weight=8.0 KN/m3) find the pressure at the interface and bottom of the tank.

34. If the atm pressure is 0.900 bar and a gauge attached to a tank reads 380 mm Hg vacuum what is absolute pressure?

35. The system in fig 10 is 20c. if atm pressure is 101.03 KPa and the abs pressure at the bottom of the tank is 231.3 KPa, What is the sp gravity of olive?

36. In fig 11 if h=25.5 inch, determine the pressure at A. the liquid has a sp gravity of 1.85

37. For the pressure vessel containing glycerin, with piezometer attached, as shown in fig 12 , what is the pressure at point A.

38. The reading of an automobile fuel gauge is proportional to the gauge pressure at the bottom of the tank (Fig 13). If the tank is 32 cm deep , and it is contaminated with 3cm of water , how many cm of air remains at the top when the gauge indicates “full” ? use sp weight of gasoline= 6670 N/m3 and air 11.8 N/m3

39. For the vertical pipe with manometer attached, shown in fig 14, find the pressure in the oil at point A.

40. Determine the reading h in fig 15 for P_A = 39 KPa vacuum if the liquid is kerosene. (Sp gravity =0.83)

41. In fig 16 Sp Gravity1=0.84 , Sp Gravity2=1.0 , h2=96mm , h1=159mm. find P_A in mm Hg gauge. If the barometer reading is 729 mm Hg, what is Pa in mm H2O absolute?

42. Assuming sea water o have a Const sp weight of 10.05 KN/m3 , What is the absolute pressure at a depth of 10 Km

43. The U-tube shown in fig 17 is 10 mm in Diameter and contain mercury, if 12.0 mL of water is pored in to the right hang leg , what are the ultimate height in the two leg

44. A manometer is attached to a conduit as shown in fig 18 . calculate pressure at point A.

45. A hydraulic press has a ram of 30cm diameter and a plunger of 5cm diameter. Find the weight lifted by the hydraulic press when the force applied at plunger is 400N.

46. A hydraulic press has a ram of 20cm diameter and plunger of 4cm in diameter. It is used for lifting a weight of 20 kN. Find the force required at the plunger.

47. An oil of a sp. Gravity 0.8 is contained in a vessel. At a point the height of oil is 20m. Find the corresponding height of water at that point.

48. The diameter of a small piston and a large piston of a hydraulic jack are 2 cm and 10 cm respectively. A force of 60 N is applied on the small piston. Find the load lifted by the large piston, when a) the piston is at the same level b) small piston is 20 cm above the large piston. The density of the liquid in the jack is 1000 kg/m3

49. A simple manometer I used to measure the pressure of oil (sp gravity 0.8) flowing in a pipe line. Its right limb is opened to the atm and left limb is connected to the pipe. The center of the pipe is 9 cm below the level of mercury (sp gravity 13.6) in the right limb. If the difference of mercury level in the two limb is 15 cm, determine the absolute pressure of oil in the pipe in N/cm2.

50. Why we can’t use water in place of mercury in barometer justify your answer with calculation.