Exam 10: Fluids

As shown in the figure, water $\text { (density } 1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } \text { ) }$ is flowing in a pipeline. At point 1 the water speed is 5.90 m/s. Point 2 is 5.20 m above point 1. The cross-sectional area of the pipe is $0.0800 \mathrm {~m} ^ { 2 }$ at point 1 and $0.0200 \mathrm {~m} ^ { 2 }$ at point 2. What is the pressure difference p 1-p 2 between points 1 and 2? Treat the water as an ideal incompressible fluid.

A $1.00 - \mathrm { m } ^ { 3 }$ object floats in water with 20.0% of its volume above the waterline. What does the object weigh out of the water? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A 200-kg flat-bottomed boat floats in fresh water, which has a density of $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ If the base of the boat is 1.42 m wide and 4.53 m long, to what depth is the bottom of the boat submerged when it carries three passengers whose total mass is 257 kg?

A pump uses a piston of 15 cm diameter that moves at 2.0 cm/s as it pushes a fluid through a pipe. What is the speed of the fluid when it enters a portion of the pipe that is 3.0 mm in diameter? Treat the fluid as ideal and incompressible.

What buoyant force does a 0.60-kg solid gold crown experience when it is immersed in water? The density of gold is $19.3 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and that of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Water flowing through a cylindrical pipe suddenly comes to a section of pipe where the diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was 32m/s, what is its speed in this smaller section if the water behaves like an ideal incompressible fluid?

One of the dangers of tornados and hurricanes is the rapid drop in air pressure that is associated with such storms. Assume that the air pressure inside of a sealed house is 1.02 atm when a hurricane hits. The hurricane rapidly decreases the external air pressure to 0.910 atm. What net outward force is exerted on a square window of the house that is 2.03 m on each side? (1.00 atm= $\left. 1.01 \times 10 ^ { 5 } \mathrm {~Pa} \right)$

A person weighing 900 N is standing on snowshoes. Each snowshoe has area $2500 \mathrm {~cm} ^ { 2 }$ and has

How many grams of ethanol $\left( \text { density } 0.80 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$ should be added to 5.0 g of chloroform (density $\left. 1.5 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$ if the resulting mixture is to have a density of $1.2 \mathrm {~g} / \mathrm { cm } ^ { 3 } ?$ Assume that the fluids do not change their volumes when they are mixed.

The deepest point of the Pacific Ocean is 11,033 m, in the Mariana Trench. What is the gauge pressure in the water at that point? The density of seawater is $1025 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

The Aswan High Dam on the Nile River in Egypt is 111 m high. What is the gauge pressure in the water at the foot of the dam? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A container has a vertical tube, whose inner radius is 24.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube -level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C , whose density is $570 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ The mass of the oil is closest to

Two horizontal pipes have the same diameter, but pipe B is twice as long as pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe B is $Q = \frac { \Delta V } { \Delta t }$ what is the flow rate in pipe A ?

A $50 - \mathrm { cm } ^ { 3 }$ block of wood is floating on water, and a $50 - \mathrm { cm } ^ { 3 }$ chunk of iron is totally submerged in the water. Which one has the greater buoyant force on it?

A polar bear of mass 200 kg stands on an ice floe that is a uniform 1.0 m thick. What is the minimum area of the floe that will just support the bear in saltwater of density $1030 \mathrm {~kg} / \mathrm { m } ^ { 3 } ?$ The density of ice is $980 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A hollow steel ball of diameter 3.0 m just barely floats in water. What is the wall thickness of the ball? $\left( \rho \mathrm { Fe } = 7.87 \mathrm {~g} / \mathrm { cm } ^ { 3 } , \rho _ { \text {water } } = 1.00 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$

A container consists of two vertical cylindrical columns of different diameter connected by a narrow horizontal section, as shown in the figure. The open faces of the two columns are closed by very light plates that can move up and down without friction. The tube diameter at A is 35.0 cm and at B it is 10.2 cm. This container is filled with oil of density $0.820 \mathrm {~g} / \mathrm { cm } ^ { 3 }$ If a 125-kg object is placed on the larger plate at A , how much mass should be placed on the smaller plate at B to balance it?.

A styrofoam sphere of radius R has a density $\rho .$ You now carefully compress the sphere so its radius is R/2 . What is the density of the compressed sphere?