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Chapter 14: Q 60P (page 401)

Models of torpedoes are sometimes tested in a horizontal pipe of flowing water, much as a wind tunnel is used to test model airplanes. Consider a circular pipe of internal diameter 25.0cmand a torpedo model aligned along the long axis of the pipe. The model has a 5.00cmdiameter and is to be tested with water flowing past it at 2.50m/s.

(a) With what speed must the water flow in the part of the pipe that is unconstricted by the model?

(b) What will the pressure difference be between the constricted and unconstricted parts of the pipe?

Short Answer

Expert verified


Hence, the pressure difference between the constricted and unconstricted parts of the pipe is

Step by step solution

01

Given data

  1. The internal diameter of the pipe,.

  2. The diameter of the torpedoes model,.

  3. The speed of the water at a constricted section of pipe,.

  4. The pipe is horizontal.

02

Determining the concept

Determine the speed of the water at the unconstricted section of the pipe using the equation of continuity. Then, using Bernoulli鈥檚 equation, find the pressure difference between the constricted and unconstricted parts of the pipe. According to Bernoulli鈥檚 equation, as the speed of a moving fluid increases, the pressure within the fluid decreases.

Formulae are as follows:

Where,pis pressure,vis velocity,his height,gis an acceleration due to gravity,his height,Ais the area, andis density.

03

(a) Determining the speed of the water at the unconstricted section of the pipe


The effective diameter of the constricted section of the pipe is,

The water flowing through the pipe obeys the equation of continuity.

Hence,

Hence, the speed of the water at the unconstricted section of the pipe is

04

 (b) Determining the pressure difference between the constricted and unconstricted parts of the pipe

The water flow obeys Bernoulli鈥檚 principle.

So,

Given that the pipe is horizontal, i.e.,hc=hu, and蟻= density of water = 1000 kg/m3,

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Most popular questions from this chapter

A large aquarium of height 5.00 mis filled with fresh water to a depth of 2.00 m. One wall of the aquarium consists of thick plastic 8.00 mwide.

By how much does the total force on that wall increase if the aquarium is next filled to a depth of 4.00 m?

How much work is done by pressure in forcing 1.4m3of water through a pipe having an internal diameter of 13mmif the difference in pressure at the two ends of the pipe is 1.0atm?

Giraffe bending to drink. In a giraffe with its head 2.0m above its heart, and its heart 2.0mabove its feet, the (hydrostatic) gauge pressure in the blood at its heart is250 torr. Assume that the giraffe stands upright and the blood density is 1.06脳103kg/m3. (a) In torr (or role="math" localid="1657260976786" mmHg), find the (gauge) blood pressure at the brain (the pressure is enough to perfuse the brain with blood, to keep the giraffe from fainting). (b) torrIn (ormmHg), find the (gauge) blood pressure at the feet (the pressure must be countered by tight-fitting skin acting like a pressure stocking). (c) If the giraffe were to lower its head to drink from a pond without splaying its legs and moving slowly, what would be the increase in the blood pressure in the brain? (Such action would probably be lethal.)

Question: To suck lemonade of density 1000 kg / m3up a straw to a maximum height of 4.0 cm , what minimum gauge pressure (in atmospheres) must you produce in your lungs?

In 1654 Otto von Guericke, inventor of the air pump, gave a demonstration before the noblemen of the Holy Roman Empire in which two teams of eight horses could not pull apart two evacuated brass hemispheres. (a) Assuming the hemispheres have (strong) thin walls, so that R in Figure may be considered both the inside and outside radius, show that the force required to pull apart the hemispheres has magnitudeF=蟺R2鈭�p, where鈭�pis the difference between the pressures outside and inside the sphere. (b) Takingas, the inside pressure asrole="math" localid="1657253356406" 0.10atm, and the outside pressure as1.00atm,find the force magnitude the teams of horses would have had to exert to pull apart the hemispheres. (c) Explain why one team of horses could have proved the point just as well if the hemispheres were attached to a sturdy wall.
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