Question

A pressurized 2-m-diameter tank of water has a 10-cm-diameter orifice at the bottom where water discharges to the atmosphere. The water level initially is 3 m above the outlet. The tank air pressure above the water level is maintained at 450 kPa absolute and the atmospheric pressure is 100 kPa Neglecting frictional effects, determine: (a) how long it will take for half of the water in the tank to be discharged; (b) the water level in the tank after 10 s

Answer 1

Answer:

A fluid is defined as a material that deforms continuously and permanently under the

application of a shearing stress.

• The pressure at a point in a fluid is independent of the orientation of the surface

passing through the point; the pressure is isotropic.

• The force due to a pressure p acting on one side of a small element of surface dA

defined by a unit normal vector n is given by −pndA.

• Pressure is transmitted through a fluid at the speed of sound.

• The units we use depend on whatever system we have chosen, and they include quantities

like feet, seconds, newtons and pascals. In contrast, a dimension is a more

abstract notion, and it is the term used to describe concepts such as mass, length and

time.

• The specific gravity (SG) of a solid or liquid is the ratio of its density to that of water

at the same temperature.

• A Newtonian fluid is one where the viscous stress is proportional to the rate of strain

(velocity gradient). The constant of proportionality is the viscosity, µ, which is a

property of the fluid, and depends on temperature.

• At the boundary between a solid and a fluid, the fluid and solid velocities are equal;

this is called the “no-slip condition.” As a consequence, for large Reynolds numbers

(>> 1), boundary layers form close to the solid boundary. In the boundary layer,

large velocity gradients are found, and so viscous effects are important.

• At the interface between two fluids, surface tension may become important. Surface

tension leads to the formation of a meniscus, drops and bubbles, and the capillary rise

observed in small tubes, because surface tension can resist pressure differences across

the interface.