19. Fluid Mechanics

Fluid Flow & Continuity Equation

Open Question
(II) A 6.0-cm-diameter horizontal pipe gradually narrows to 4.5 cm. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 36.5 kPa and 22.6 kPa, respectively. What is the volume rate of flow?
Open Question
A 2.0 mL syringe has an inner diameter of 6.0 mm, a needle inner diameter of 0.25 mm, and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine into a patient whose blood pressure is 140/100 .b. The nurse empties the syringe in 2.0 s. What is the flow speed of the medicine through the needle?
Multiple Choice
Two hoses have been connected together. The first hose has a diameter of 4 cm, and the second has a diameter of $2 . 5 cm .$ If the water exits the narrower hose at a speed of $3.4 m/s$ , how quickly is the water moving inside the wider hose?
Multiple Choice
A blood vessel has a radius of $5 . 0 mm .$ This blood vessel divides into two, each having a radius of $4 . 0 mm$ . If the speed of the blood just before the split is $0.31 m/s$ , what is the speed of blood just after the split?
Open Question
Home Repair. You need to extend a 2.50-inch-diameter pipe, but you have only a 1.00-inch-diameter pipe on hand. You make a fitting to connect these pipes end to end. If the water is flowing at 6.00 cm/s in the wide pipe, how fast will it be flowing through the narrow one?
Open Question
A soft drink (mostly water) flows in a pipe at a beverage plant with a mass flow rate that would fill 220 0.355-L cans per minute. At point 2 in the pipe, the gauge pressure is 152 kPa and the cross-sectional area is 8.00 cm^2. At point 1, 1.35 m above point 2, the cross-sectional area is 2.00 cm^2. Find the (b) volume flow rate. (c) flow speeds at points 1 and 2.
Open Question
A shower head has 20 circular openings, each with radius 1.0 mm. The shower head is connected to a pipe with radius 0.80 cm. If the speed of water in the pipe is 3.0 m/s, what is its speed as it exits the shower-head openings?
Open Question
Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At point 1 the cross-sectional area of the pipe is 0.070 m^2, and the magnitude of the fluid velocity is 3.50 m/s. (c) Calculate the volume of water discharged from the open end of the pipe in 1.00 hour.
Open Question
A tree loses water to the air by the process of transpiration at the rate of 110 g/h. This water is replaced by the upward flow of sap through vessels in the trunk. If the trunk contains 2000 vessels, each 100 μm in diameter, what is the upward speed in mm/s of the sap in each vessel? The density of tree sap is 1040 kg/m³.
Open Question
A nuclear power plant draws 3.0 x 10⁶ L/min of cooling water from the ocean. If the water is drawn in through two parallel, 3.0-m-diameter pipes, what is the water speed in each pipe?
Open Question
(II) A fish tank has dimensions 36 cm wide by 1.0 m long by 0.60 m high. If the filter should process all the water in the tank once every 2.5 h, what should the flow speed be in the 3.0-cm-diameter input tube for the filter?
Open Question
Four lawn sprinkler heads are fed by a 1.9-cm-diameter pipe. The water comes out of the heads at an angle of 35° to the horizontal and covers a radius of 5.0 m.

(c) How fast is the water flowing inside the 1.9-cm-diameter pipe?
Open Question
(I) Calculate the average speed of blood flow in the major arteries of the body, which have a total cross-sectional area of about 2.0 cm² . Use the data of Example 13–14.
Open Question
(II) Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.78 m/s through a pipe 5.0 cm in diameter. The pipe tapers down to 2.8 cm in diameter by the top floor, 16 m above (Fig. 13–57), where the faucet has been left open. Calculate the flow velocity and the gauge pressure in the pipe on the top floor. Assume no branch pipes and ignore viscosity.
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Open Question
(III) (a) Show that the flow speed measured by a venturi meter (see Fig. 13–32) is given by the relation

v₁ = A₂ √ 2 (P₁ - P₂) / ρ (A²₁ - A²₂) .

(b) A venturi meter is measuring the flow of water; it has a main diameter of 3.5 cm tapering down to a throat diameter of 1.0 cm. If the pressure difference is measured to be 18 mm-Hg, what is the speed of the water entering the venturi throat?

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