Monday 21 March 2016

Typical Numerical Exercises of Fluid Statics

1. A 80 Kg man has a total foot imprint area of 300 cm2. Determine the pressure this man exerts on the ground if (a) he stands on both feet and (b) he stands on one foot. 
2. Blood pressure is usually measured by wrapping a closed air-filled jacket equipped with a pressure gauge around the upper arm of a person at the level of the heart. Using a mercury manometer and a stethoscope, the systolic pressure (the maximum pressure when the heart is pumping) and the diastolic pressure (the minimum pressure when the heart is resting) are measured in mm of Hg. The systolic and diastolic pressures of a healthy person are about 120 mm of Hg and 80 mm of Hg, respectively, and are indicated as 120/80. Express both of these gauge pressures in kPa, and meters of water column.
3. Consider a 1.8-m-tall man standing vertically in water and completely submerged in a pool. Determine the difference between the pressures acting at the head and at the toes of this man, in kPa.
4. A closed tank is 8m high. It is filled with Glycerine up to a depth of 3.5m and linseed oil to another 2.5m. The remaining space is filled with air under a pressure of 150 kPa. If a pressure gauge is fixed at the bottom of the tank what will be its reading. Also calculate absolute pressure. Take relative density of Glycerine and Linseed oil as 1.25 and 0.93 respectively.
5. The hydraulic lift in a car repair shop has an output diameter of 30 cm and is to lift cars up to 2000 kg. Determine the fluid gauge pressure that must be maintained in the reservoir.
6. A heavy car plunges into a lake during an accident and lands at the bottom of the lake on its wheels. The door is 1.2 m high and 1 m wide, and the top edge of the door is 8 m below the free surface of the water. Determine the hydro static force on the door and the location of the pressure center, if (a) the car is well-sealed and it contains  air at atmospheric pressure and (b) the car is filled with water.
7. Consider a 4-m-long, 4-m-wide, and 1.5-m-high above ground swimming pool that is filled with water to the rim. (a) Determine the hydro-static force on each wall and the distance of the line of action of this force from the ground. (b) If the height of the walls of the pool is doubled and the pool is filled, will the hydro static force on each wall double or quadruple? Why?
8. A room in the lower level of a cruise ship has a 30-cm-diameter circular window. If the midpoint of the window is 5 m below the water surface, determine the hydro static force acting on the window, and the pressure center. Take the specific gravity of seawater to be 1.025.

Thursday 3 March 2016

FLUID MECHANICS FACTS


Will what works in air work in water?

For the past few years a San Francisco company has been working on small, maneuverable submarines designed to travel through water using wings, controls, and thrusters that are similar to those on jet airplanes. After all, water (for submarines) and air (for airplanes) are both fluids, so it is expected that many of the principles governing the flight of airplanes should carry over to the “flight” of winged submarines. Of course, there are differences. For example, the submarine must be designed to withstand external pressures of nearly 700 pounds per square inch greater than that inside the vehicle. On the other hand, at high altitude where commercial jets fly, the exterior pressure is 3.5 psi rather than standard sea level pressure of 14.7 psi, so the vehicle must be pressurized internally for passenger comfort. In both cases, however, the design of the craft for minimal drag, maximum lift, and efficient thrust is governed by the same fluid dynamic concepts.

How long is a foot?

Today, in the United States, the common length unit is the foot, but throughout antiquity the unit used to measure length has quite a history. The first length units were based on the lengths of various body parts. One of the earliest units was the Egyptian cubit, first used around 3000 B.C. and defined as the

length of the arm from elbow to extended fingertips. Other measures followed, with the foot simply taken as the length of a man’s foot. Since this length obviously varies from person to person it was often “standardized” by using the length of the current reigning royalty’s foot. In 1791 a special French commission proposed that a new universal length unit called a meter (metre) be defined as the distance of one-quarter of the earth’s meridian (north pole to the equator) divided by 10 million. Although controversial, the meter was accepted in 1799 as the standard. With the development of advanced technology, the length of a meter was redefined in 1983 as the distance traveled by light in a vacuum during the time interval of s. The foot is now defined as 0.3048 meters. Our simple rulers and yardsticks indeed have an intriguing history.

Units and space travel A NASA spacecraft, the Mars Climate Orbiter, was launched in December 1998 to study the Martian geography and weather patterns. The spacecraft was slated to begin orbiting Mars on September 23, 1999. However, NASA officials lost communication with the spacecraft early that day and it is believed that the spacecraft broke apart or overheated because it came too close to the surface of Mars. Errors in the maneuvering commands sent from earth caused the Orbiter to sweep within 37 miles of the surface rather than the intended 93 miles. The subsequent investigation revealed that the errors were due to a simple mix-up in units. One team controlling the Orbiter used SI units whereas another team used British Gravitational (BG) System units. This costly experience illustrates the importance of using a consistent system of units.

This water jet is a blast Usually liquids can be treated as incompressible fluids. However, in some applications the compressibility of a liquid can play a key role in the operation of a device. For example, a water pulse generator using compressed water has been developed for use in mining operations. It can fracture rock by producing an effect comparable to a conventional explosive such as gunpowder. The device uses the energy stored in a water-filled accumulator to generate an ultrahigh-pressure water pulse ejected through a 10- to 25-mm-diameter discharge valve. At the ultrahigh pressures used (300 to 400 MPa, or 3000 to 4000 atmospheres), the water is compressed (i.e., the volume reduced) by about 10 to 15%. When a fast-opening valve within the pressure vessel is opened, the water expands and produces a jet of water that upon impact with the target material produces an effect similar to the explosive force from conventional explosives. Mining with the water jet can eliminate various hazards that arise with the use of conventional chemical explosives, such as those associated with the storage and use of explosives and the generation of toxic gas by-products that require extensive ventilation.

Spreading of oil spills With the large traffic in oil tankers there is great interest in the prevention of and response to oil spills. As evidenced by the famous Exxon Valdez oil spill in Prince William Sound in 1989, oil spills can create disastrous environmental problems. It is not surprising that much attention is given to the rate at which an oil spill spreads. When spilled, most oils tend to spread horizontally into a smooth and slippery surface, called a slick. There are many factors which influence the ability of an oil slick to spread, including the size of the spill, wind speed and direction, and the physical properties of the oil. These properties include surface tension, specific gravity, and viscosity. The higher the surface tension the more likely a spill will remain in place. Since the specific gravity of oil is less than one, it floats on top of the water, but the specific gravity of an oil can increase if the lighter substances within the oil evaporate. The higher the viscosity of the oil the greater the tendency to stay in one place.
Giraffe’s blood pressure A giraffe’s long neck allows it to graze up to 6 m above the ground. It can also lower its head to drink at ground level. Thus, in the circulatory system there is a significant hydrostatic pressure effect due to this elevation change. To maintain blood to its head throughout this change in elevation, the giraffe must maintain a relatively high blood pressure at heart level—approximately two and a half times that in humans. To prevent rupture of blood vessels in the high-pressure lower leg regions, giraffes have a tight sheath of thick skin over their lower limbs which acts like an elastic bandage in exactly the same way as do the g-suits of fighter pilots. In addition, valves in the upper neck prevent back flow into the head when the giraffe lowers its head to ground level. It is also thought that blood vessels in the giraffe’s kidney have a special mechanism to prevent large changes in filtration rate when blood pressure increases or decreases with its head movement.

Weather, barometers, and bars One of the most important indicators of weather conditions is atmospheric pressure. In general, a falling or low pressure indicates bad weather; rising or high pressure, good weather. During the evening TV weather report in the United States, atmospheric pressure is given as so many inches (commonly around 30 in.). This value is actually the height of the mercury column in a mercury barometer adjusted to sea level. To determine the true atmospheric pressure at a particular location, the elevation relative to sea level must be known. Another unit used by meteorologists to indicate atmospheric pressure is the bar, first used in weather reporting in 1914, and defined as 105 Nm2 . The definition of a bar is probably related to the fact that standard sea level pressure is 1.0133 X 105 Nm2 , that is, only slightly larger than one bar. For typical weather patterns, “sea-level equivalent” atmospheric pressure remains close to one bar. However, for extreme weather conditions associated with tornadoes, hurricanes, or typhoons, dramatic changes can occur. The lowest atmospheric sea-level pressure ever recorded was associated with a typhoon, Typhoon Tip, in the Pacific Ocean on October 12, 1979. The value was 0.870 bars (25.8 in. Hg).

Tire pressure warning Proper tire inflation on vehicles is important for more than ensuring long tread life. It is critical in preventing accidents such as rollover accidents caused by under inflation of tires. The National Highway Traffic Safety Administration is developing a regulation regarding four-tire tire-pressure monitoring systems that can warn a driver when a tire is more than 25 percent under inflated. Some of these devices are currently in operation on select vehicles; it is expected that they will soon be required on all vehicles. A typical tire-pressure monitoring system fits within the tire and contains a pressure transducer (usually either a piezo-resistive or a capacitive type transducer) and a transmitter that sends the information to an electronic control unit within the vehicle. Information about tire pressure and a warning when the tire is under inflated is displayed on the instrument panel. The environment (hot, cold, vibration) in which these devices must operate, their small size, and required low cost provide challenging constraints for the design engineer.

Miniature, exploding pressure vessels Our daily lives are safer because of the effort put forth by engineers to design safe, lightweight pressure vessels such as boilers, propane tanks, and pop bottles. Without proper design, the large hydrostatic pressure forces on the curved surfaces of such containers could cause the vessel to explode with disastrous consequences. On the other hand, the world is a more friendly place because of miniature pressure vessels that are designed to explode under the proper conditions—popcorn kernels. Each grain of popcorn contains a small amount of water within the special, impervious hull (pressure vessel) which, when heated to a proper temperature, turns to steam, causing the kernel to explode and turn itself inside out. Not all popcorn kernels have the proper properties to make them pop well. First, the kernel must be quite close to 13.5% water. With too little moisture, not enough steam will build up to pop the kernel; too much moisture causes the kernel to pop into a dense sphere rather than the light fluffy delicacy expected. Second, to allow the pressure to build up, the kernels must not be cracked or damaged.

Pressurized eyes Our eyes need a certain amount of internal pressure in order to work properly, with the normal range being between 10 and 20 mm of mercury. The pressure is determined by a balance between the fluid entering and leaving the eye. If the pressure is above the normal level, damage may occur to the optic nerve where it leaves the eye, leading to a loss of the visual field termed glaucoma. Measurement of the pressure within the eye can be done by several different noninvasive types of instruments, all of which measure the slight deformation of the eyeball when a force is put on it. Some methods use a physical probe that makes contact with the front of the eye, applies a known force, and measures the deformation. One non contact method uses a calibrated “puff” of air that is blown against the eye. The stagnation pressure resulting from the air blowing against the eyeball causes a slight deformation, the magnitude of which is correlated with the pressure within the eyeball.



















Fluid Mechanics Assignment questions

 
1. Define the following terms with their units.
i. Specific weight  ii. Specific gravity         iii. Surface Tension   iv. Dynamic viscosity  v. Kinematic viscosity.
2. How does the dynamic viscosity of (a) liquids and (b) gases vary with temperature?
3. What is manometer? How they are classified?
4. Calculate specific weight, density, specific volume and specific gravity of one liter of liquid which weighs 7.836 N.                                                                           
5. A cubical block of sides 1m & weighing 350N slides down an inclined plane with a uniform velocity of 1.5 m/s. The inclined plane is inclined at 30ْْ° to horizontal & has an oil film of 1mm thickness. Calculate the dynamic viscosity of oil.          
6. In a 50mm long journal bearing arrangement, the clearance between the two at concentric condition is 0.1mm. The shaft is 2.0mm in diameter and rotates at 3000 rpm. The dynamic viscosity of the lubricant used is 0.01 pas and the velocity variation in the lubricant is linear. Considering the lubricant to be Newtonian, calculate the frictional torque the journal has to overcome and the corresponding power loss.
7. Calculate the capillary rise in a glass tube of 2.5 mm diameter when immersed vertically in (a) water and (b) mercury. Take surface tensions 0.0725 N/m for water and 0.52 N/m for mercury. The angle of contact for mercury is 130°.
8. A 80 Kg man has a total foot imprint area of 300 cm2. Determine the pressure this man exerts on the ground if (a) he stands on both feet and (b) he stands on one foot.
9. Consider a 1.8-m-tall man standing vertically in water and completely submerged in a pool. Determine the difference between the pressures acting at the head and at the toes of this man, in kPa.
10. A U tube manometer is used to measure the pressure of water in a pipeline, which is in excess of atmospheric pressure. The right limb of the manometer contains mercury and is open to atmosphere. The contact between water and mercury is in the left limb. Determine the pressure of water in the main line, if the difference in level of mercury in the limbs of U tube is 10 cm and the free surface of mercury is in level with the centre of the pipe. If the pressure of water in pipeline is reduced to 9810 Pa, calculate the new difference in the level of mercury. Sketch the arrangements in both cases.