Mechanical Engineering Tutorials

Discussion

Laboratory

Calibration of Bourdon Pressure Gauge

Sample Problems

An open tank is filled with 2-m of water and 1.5-m of kerosene(SG=0.82). Determine (a) the interface pressure and (b) the pressure at the bottom of the tank.

A closed tank contained compressed air and oil (SG_oil = 0.90). A U-tube manometer using mercury (SG_Hg = 13.6) is connected to the tank. The column height are h₁ = 36-in, h₂ = 6-in and h₃ = 9-in. Determine the pressure of the air inside the tank.

A pressure cooker cooks a lot faster than an ordinary pan by maintaining a higher pressure and temperature inside. The lid of the pressure cooker is well sealed, and steam can escape only through an opening in the middle of the lid. A separate piece of certain mass, the petcock, sits on top of this opening and prevents steam from escaping until the pressure force overcomes the weight of the petcock. The periodic escape of the steam in this manner prevents any potentially dangerous pressure build up and keeps the pressure inside at a constant value. Determine the mass of the petcock of the pressure cooker whose operating pressure is 100 kPa gage and has opening cross-sectional area of 4mm². Assume an atmospheric pressure of 101 kPa.

Discussion

Archimedes' Principle states that when an object fully or partially submerged in a liquid, it experiences a buoyant force (or upthrust) which is equal to the weight of the liquid displaced by the object.

Sample Problems

A wooden block with a cross section of 0.50-m x 0.50-m floats in water with 0.30-m projecting above the water surface. If this block is transferred in oil of specific gravity of 0.85, the wooden object floats 0.22-m projecting above the oil surface. Calculate the height of the wooden object.

A bargain hunter purchases a "gold" crown at a flea market. After she comes home, she hangs it from scale and found its weight to be 7.84 N. She then weigh the crown while it is submersed in water, and now the scale reads 6.86 N. Is the crown made of pure gold? 

Discussion

The force exerted by static fluid on the surfaces in contact with fluid is called hydrostatic pressure. It is always normal to the contact surface. The center of pressure is the defined as the point of application of the total pressure on the surface.

Sample Problems

If a rectangular plate of height 10-ft and base 5-ft is vertical and submerged in water with its base at the liquid surface. Find the hydrostatic force and the depth of its center of pressure.

Discussion

The criterion of stability of a floating body is metacenter, which is an imaginary center with respect to the center of gravity G. The distance between the metacenter and center of gravity is known as metacentric height.

Sample Problems

A rectangular raft 10 m wide, 15 m length and 5 m height has a draft of 2.6 m. If the center of gravity of the raft is 3 m above the bottom of the raft, find (a) the initial metacentric height.

IMPORTANT NOTES

Determine the final metacentric height and the righting moment if the raft is tilted until its opposite end is just submerged in water.

Discussion

Bernoulli's principle states that in an ideal and incompressible fluid, when the flow is steady and continuous, the sum of the pressure head, velocity head and elevation head of the fluid is constant at all points in the flow system.

Laboratory

Sample Problems

A water is shooting out vertically from a pipe nozzle. Calculate the height above the nozzle opening to which the water will shoot.

A closed tank of a fire engine is partly filled with water, the air space above being under pressure. A 6-cm bore connected to the tank discharges on the roof of the building 2.5-m above the level of water in the tank. Assume no losses due to friction. Determine the pressure which must be maintained in the tank to deliver 20 L/sec on the roof.

Discussion

Coefficient of Velocity, Cv is defined as the ratio between the actual velocity of a jet of liquid at vena contracta to the theoretical velocity.

Coefficient of Contraction, Cc is defined as the ratio of the area of jet at vena contracta to the area of the orifice.

Coefficient of Discharge, Cd is defined as the ratio of the actual discharge through an orifice to the theoretical discharge.

Laboratory

Discussion

Laboratory

Discussion

Sample Problem

A parallel piping system has a main pipe which divides into two branches and again join together downstream to form a single pipe. The length and diameter for the first parallel pipe are 2000 m and 1 m, respectively, while the length and diameter of second parallel pipe are 2000 m and 0.8 m. Find the rate of flow in each parallel pipe, if the total flow in the main is 3.0 m³/s. The coefficient of friction for each parallel pipe is same and equal to 0.005.