What is the pressure drop due to the Bernoulli Effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s? (b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)

Suppose you have a coffee mug with a circular cross-section and vertical sides (uniform radius). What is its inside radius if it holds 375 g of coffee when filled to a depth of 7.50 cm? Assume coffee has the same density as water.

If a person's body has a density of 995 kg/m³, what fraction of the body will be submerged when floating gently in (a) freshwater? (b) In salt water with a density of 1027 kg/m³?

Gold is sold by the troy ounce (31.103 g). What is the volume of 1 troy ounce of pure gold?

What is the pressure drop due to the Bernoulli effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s?

A container of water has a cross-sectional area of $A=0.1 \mathrm{~m}^2$. A piston sits on top of the water (see the following figure). There is a spout located $0.15 \mathrm{~m}$ from the bottom of the tank, open to the atmosphere, and a stream of water exits the spout. The cross sectional area of the spout is $A_s=7.0 \times 10^{-4} \mathrm{~m}^2$. (a) What is the velocity of the water as it leaves the spout? (b) If the opening of the spout is located $1.5 \mathrm{~m}$ above the ground, how far from the spout does the water hit the floor? Ignore all friction and dissipative forces.

Gold is sold by the troy ounce (31.103 g). What is the volume of 1 troy ounce of pure gold?

Consider a river that spreads out in a delta region on its way to the sea. Construct a problem in which you calculate the average speed at which water moves in the delta region, based on the speed at which it was moving up river. Among the things to consider are the size and flow rate of the river before it spreads out and its size once it has spread out. You can construct the problem for the river spreading out into one large river or into multiple smaller rivers.

Water towers store water above the level of consumers for times of heave use, eliminating the need for high-speed pumps. How high above a user must the water level be to create a gauge pressure of

$$3.00 × 10^5 N/m^2?$$

What force must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2000-kg car (a large car) resting on the slave cylinder? The master cylinder has a 2.00-cm diameter and the slave has a 24.0-cm diameter.

Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mph) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli equation on a roof having an area of 220 m²? Typical air density in Boulder is 1.14 kg/m³, and the corresponding atmospheric pressure is

$$8.89 × 10^4 N/m^2.$$

(Bernoulli's principle assumes laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)

(a) Calculate the approximate force on a square meter of sail, given the horizontal velocity of the wind is 6.00 m/s parallel to its front surface and 3.50 m/s along its back surface. Take the density of air to be $1.29\ \mathrm{kg} / \mathrm{m}^{3}.$ (The calculation, based on Bernoulli's principle, is approximate due to the effects of turbulence.) (b) Discuss whether this force is great enough to be effective for propelling a sailboat.

A certain hydraulic system is designed to exert a force 100 times as large as the one put into it. (a) What must be the ratio of the area of the slave cylinder to the area of the master cylinder? (b) What must be the ratio of their diameters? (c) By what factor is the distance through which the output force moves reduced relative to the distance through which the input force moves? Assume no losses to friction.

Suppose you stand with one foot on ceramic flooring and one foot on a wool carpet, making contact over an area of $80.0 \mathrm{~cm}^2$ with each foot. Both the ceramic and the carpet are $2.00 \mathrm{~cm}$ thick and are $10.0^{\circ} \mathrm{C}$ on their bottom sides. At what rate must heat transfer occur from each foot to keep the top of the ceramic and carpet at $33.0^{\circ} \mathrm{C}$ ?