Ch. 15 Fluids. Fluids. Substances that flow readily, usually from high pressure to low pressure. They take the shape of the container rather than retain their shape. We refer both liquids and gases as fluids. Density. Is the mass of a substance divided by the volume of that substance.
or g / cm3
D = 4.50 g/cm3
U: V = ?
E: D = m / V V = m/D
S: V = 2.16 / 4.50 g/cm3
S: V = 0.48 cm3
w = 60 cm = 0.6 m
P = 40,000 Pa
U: F = ?
E: F = PA
A = Lw
A = (.4)(.6)
A = 0.24 m2
F = 9600 N
The pressure of the earth’s atmosphere pushing down on you.
Sample ProblemCalculate the net force on an airplane window if cabin pressure is 90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide.
Since pressure acts equally in all directions, gauge pressure is used to deal with this.
The deeper the body of water or you go, the more water there is on top of you per square inch.
Phyd = rgh
r – weight density of liquid
Pressure applied to a fluid in a closed container is transmitted equally
By Pascal’s Principle:
P1 = P2
F1/A1 = F2/A2
So if the 2nd area is increased by a factor of 25.
F1d1 = F2d2
U: F1 = ?
E: F1/A1 = F2/A2
F1 = F2A1/A2
S: F1 = 2666.7 N
Is the upward force equal to the weight of the fluid displaced.
The buoyant force is equal to the weightof the liquid displaced. Immersion: all or part under water.Submersion: completely under water
Vs – volume of the solid
rs – density of solid
rf – density of fluid
Sample problem: Assume a wooden raft has 80.0% of the density of water. The dimensions of the raft are 6.0 meters long by 3.0 meters wide by 0.10 meter tall. How much of the raft rises above the level of the water when it floats? (density of water is 1000 kg/m3)
Is the ratio of any substance’s density to the density of water.
Specific a substance
V = Avt
V: volume of fluid (m3)
A: cross sectional areas at a point in the pipe (m2)
v: speed of fluid flow at a point in the pipe (m/s)
t: time (s)
r1A1v1 = r2A2v2
Use for gases.
A1v1 = A2v2
Sample problem: A pipe of diameter 6.0 cm has fluid flowing through it at 1.6 m/s. How fast is the fluid flowing in an area of the pipe in which the diameter is 3.0 cm? How much water per second flows through the pipe?
Sample problem: The water in a canal flows 0.10 m/s where the canal is 12 meters deep and 10 meters across. If the depth of the canal is reduced to 1.5 meters at an area where the canal narrows to 5.0 meters, how fast will the water be moving through this narrower region?
The sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous incompressible fluid in streamline flow.
Sample Problem: Water travels through a 9.6 cm diameter fire hose with a speed of 1.3 m/s. At the end of the hose, the water flows out of a nozzle whose diameter is 2.5 cm. What is the speed of the water coming out of the nozzle? If the pressure in the hose is 350 kPa, what is the pressure in the nozzle?
P1 + r g h1 + ½ rv12 = P2 + r g h2 + ½ rv22
Patm + r g h1 + 0 = Patm + 0 + ½ rv22
Sample Problem: An above-ground swimming pool has a hole of radius 0.10 cm in the side 2.0 meters below the surface of the water. How fast is the water flowing out of the hole? How much water flows out each second?