A block of aluminum has a size of \(10 \,cm \times 5 \,cm \times 2 \,cm\text{.}\)
What is the mass?
What is its weight?
If immersed in water, what would be the volume of the displaced water?
What would be the weight of the displaced water?
How large a force would be required to keep the block from sinking in the water?
2.
A cube of wood 10 cm on a side is floating in oil of specific gravity 0.8 with its top face 2 cm above the surface of the oil. What is
the density of the oil,
the volume of the displaced oil,
the mass of the displaced oil,
the weight of the displaced oil,
the weight of the cube,
the volume of the cube,
the density of the cube,
the pressure at the bottom of the cube, and
the force exerted by the oil on the bottom of the cube?
3.
An aluminum weight of mass 200 g is attached by a short string to the bottom of a float of density \(0.3 g/cm^{3}\) which is supported by another string attached to a mass balance. When both the weight and the float are completely immersed in water the balance reads 50 g. What is
the volume of the float,
the mass of the float,
the buoyant force of the water on the float, and
the buoyant force of the water on the aluminum weight.
What would the balance read if only the weight were under water?
4.
The weight density of fresh water is \(62.4 \,lb/ft^{3}\) and the specific gravity of ice is 0.917. What is the minimum size (in feet) of a square slab of ice 1 ft thick that would support a man weighing 180 lbs?
5.
A hang glider has a wing area of \(165 \,ft^{2},\) weighs 70 lb (pounds), and caries a pilot weighing 200 lb with his equipment. If the velocity of the air under the wing is half that over the top, what is the average airspeed of the glider in miles per hour? Hint: This problem can be worked in the FPS system by using the fact that the specific gravity of air is \(1.29 \times 10^{-3}\) and the weight density of water is \(62.4 \,lb/ft^{3}\text{.}\)
6.
Water is flowing through a pipe with a constriction. The area of the narrow section is one half the area of the wide section. If the velocity of the incompressible fluid is \(3.2 \,m/s\) in the wide section, then what is the velocity of the fluid in the narrow section?
7.
A hose lying on the ground has water coming out of it at a speed of \(5.4 m/s.\) If the nozzle of the hose is lifted to a height of 1.3 m above the ground. Find the speed of water coming out of the hose.
8.
A large tank of water open to the air at the top has a hose attached to its bottom with a nozzle opening of diameter 0.5 cm. The velocity of the water leaving the nozzle is 6 m/s.
How high would the water squirt if the nozzle were aimed straight up?
What is the volume flow rate of the water leaving the tank?
What is the pressure in the water as it leaves the nozzle?
What is the pressure in the water at the top of the tank?
What is the velocity of the water at the top of the tank?
What is the height of the water in the tank?
If the diameter of the hose between the tank and nozzle is 1 cm, what is the velocity of the water in the hose?
What is the gauge pressure in the hose?
What is the absolute pressure in the hose?
9.
A balloon filled with helium gas is floating in air with acceleration \(a\text{.}\) If the density of air and helium gas is \(1.23 \,kg/m^{3}\) and \(0.42 \,kg/m^{3}\text{,}\) respectively and volume of balloon is \(0.075 \,m^{3}.\) Find the value of \(a.\)
Viscosity.
10.
The velocity of water in river is 5m/s at the surface. If river is 5 m deep, find the shear stress between the horizontal layers of water. The viscosity of water is \(10^{-3} \) poiseullie. [1 poiseullie = 10 pise]
11.
The flow rate of a viscous fluid through a hose is measured to be \(2\times 10^{-5} \,m^{3}/s.\) The length of the hose is 1.8 m, the viscosity of the fluid is \(0.072 \,N/m^{2},\) and the pressure difference across the hose is 55 Pa. Determine the radius of the hose.
12.
An air bubble of radius 1 mm is allowed to rise through a long cylindrical tube of a viscous liquid of radius 5 cm and travels at a steady rate of 2 cm/s. If the density of the liquid is \(1.5 \,g/cm^{3}\text{,}\) find its viscosity.
13.
An oil drop of radius \(2\times 10^{-5} \,m\) and density \(1.2 \times 10^{3} \,kg/m^{3}\) is falling freely in air of viscosity \(1.8\times 10^{-5} \,Pa.s.\) How much is the viscous force is acting on the drop at that speed? Neglect buoyancy on drop due to air.
14.
A 1.5 liter of viscous fluid is draining through a needle will take 25 minutes. If the needle diameter is increased by 20\%, how long will it take to drain the bottle?
15.
Calculate the viscosity of an oil which is used for lubrication between a plate of size 0.8m by 0.8 m inclined plane with angle of inclination \(30^{o} \text{.}\) The weight of the square plate is 300 N and it slides down the plane with uniform velocity of 0.3 m/s. The thickness of oil film is 1.5 mm.
Surface Tension.
16.
The base of an insect’s leg is approximately spherical in shape with a radius of about \(2.0\times 10^{-5} \,m.\) The mass of the insect is \(3.00\times 10^{-6} \,kg\) and is supported equally by six legs. Calculate the contact angle \(\theta\text{.}\) The coefficient of surface tension is 0.072 N/m.
17.
A circular loop of wire and a pan of soapy water is used to produce a soap bubble whose radius is 1.0 mm. The surface tension of the soapy water is \(\gamma = 2.5 \times 10^{-2} \,N/m.\) Determine the pressure difference between the inside and outside of the bubble.
The same soapy water is used to produce a spherical droplet whose radius is 0.50 mm. Find the pressure difference between the inside and outside of the droplet.
Hint.
If the bubble and drop had the same radius, then the pressure difference between the inside and outside of the bubble to be twice as large as that for the drop. Since a spherical drop of liquid has only one surface, rather than two surfaces, for there is no air within it.
18.
A circular ring of radius = 5.0 cm is immersed in the liquid and then pulled upward, so a film is formed between the ring and the liquid. An upward force of \(3.6 \times 10^{-2} N \) is required in addition to the weight of the ring to lift them to the point where the film just breaks. What is the surface tension of the liquid?
19.
A bubble of air in water (\(\gamma = 0.073 \,N/m\) ) has a radius of 0.10 mm. Find the difference in pressures between the inside and outside of the bubble.
20.
A drop of oil (\(\gamma = 0.0320 \,N/m\)) has a radius of 0.01 mm. The drop is located a distance of 2 m below the surface of fresh water. The atmospheric pressure above the water is \(1.01 \times 10^{5} \,Pa\text{.}\)
What is the absolute pressure in the water at this depth?
Determine the absolute pressure inside the oil drop.
21.
A needle of length 3.2 cm is placed gently on the surface of the water (\(\gamma =0.073 \,N/m\)) so that it can float on the water. What is the weight of the heaviest needle that can be used in this demonstration?
22.
A glass plate of length 10 cm and thickness 0.2 cm is pulled up from a liquid of surface tension 0.07 N/m, find the force with which it is pulled up. Assume the angle of contact to be zero.
