A differential equation describing the height h of a fluid level in a cylindrical tank of the radiusRlosing the fluid through a circular hole in the bottom with a radius r is dhRdt-r/2ghwhere g is free-fall acceleration. How much time will it take for the fluid to be completely drainedfrom the tank, if initially the tank was filled to a height of H.

Given information:The differential equation of height “h” in a cylindrical tank:

Answered: A differential equation describing the…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter15: Fluids

Section: Chapter Questions

Problem 44PQ: Water enters a smooth, horizontal tube with a speed of 2.0 m/s and emerges out of the tube with a...

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Figure 11.35(a) shows the effect of tube radius on the height to which capillary action can raise a fluid. (a) Calculate the height h for water in a glass tube with a radius of 0.900 cm—a rather large tube like the one on the left. (b) What is the radius of the glass tube on the right if it raises water to 4.00 cm?
Archimedes' principle can be used to calculate the density of a fluid as well as that of a solid. Suppose a chunk of iron with a mass of 390.0 g in air is found to have an apparent mass of 350.5 g when completely submerged in an unknown liquid. (a) What mass of fluid does the iron displace? (b) What is the volume of iron, using its density as given in Table 11.1 (c) Calculate the fluid's density and identify it.
(a) Convert normal blood pressure readings of 120 over 80 mm Hg to newtons per meter squared using be relationship for pressure due to the weight of a fluid (p=hg) rater a conversion factor. (b) Explain why be blood pressure of an infant would likely be smaller than that of an adult. Specifically, consider the smaller height to which blood mast be pumped.
Figure P15.52 shows a Venturi meter, which may be used to measure the speed of a fluid. It consists of a Venturi tube through which the fluid moves and a manometer used to measure the pressure difference between regions 1 and 2. The fluid of density tube moves from left to right in the Venturi tube. Its speed in region 1 is v1, and its speed in region 2 is v2. The necks cross-sectional area is A2, and the cross-sectional area of the rest of the tube is A1. The manometer contains a fluid of density mano. a. Do you expect the fluid to be higher on the left side or the right side of the manometer? b. The speed v2 of the fluid in the neck comes from measuring the difference between the heights (yR yL) of the fluid on the two sides of manometer. Derive an expression for v2 in terms of (yR yL), A1, A2, tube, and mano. FIGURE P15.52
Prove that the speed of an incompressible fluid through a constriction, such as in a Venturi tube, increases by a factor equal to the square of the factor by which the diameter decreases. (The converse applies for flow out of a constriction into a larger-diameter region.)
Suppose water is raised by capillary action to a height of 5.00 cm in a glass tube. (a) To what height will it be raised in a paraffin tube of the same radius? (b) In a silver tube of the same radius?
What is the pressure inside an alveolus having a radius of 2.50104 m if the surface tension of the fluid-lined wall is the same as for soapy water? You may assume the pressure is the same as that created by a spherical bubble.
(a) Using Bernoulli's equation, show that the measured fluid speed v for a pitot tube, like the one in Figure 12.7(b), is given by v=( 2gh)1/2 , where h is the height of the manometer fluid, is the density of the manometer fluid, is the density of the moving fluid, and g is the acceleration due to gravity. (Note that v is indeed proportional to the square root of h, as stated in the text.) (b) Calculate v for moving air if a mercury manometer's h is 0.200 m. Figure 12.7 Measurement of fluid speed based on Bernoulli's principle. (a) A manometer is connected to two that are close together and small enough not to disturb the flow. Tube 1 is open at the end facing the flow. A dead spot having zero speed is created there. Tube 2 has an opening on the side, and so the fluid has a speed V across the opening; thus, pressure there drops. The difference in pressure at the manometer is 12v22 , and so h is proportional to 12v22 . (b) This type of velocity measuring device is a Prandtl tube, also known as a pitot tube.
Water enters a smooth, horizontal tube with a speed of 2.0 m/s and emerges out of the tube with a speed of 8.0 m/s. Each end of the tube has a different cross-sectional radius. Find the ratio of the entrance radius to the exit radius.
(a) Verify that a 19.0% decrease in laminar flow through a tube is caused by a 5.00% decrease in radius, assuming that all other factors remain constant, as stated in the text. (b) What increase in flow is obtained from a 5.00% increase in radius, again assuming all other factors remain constant?
A certain man has a mass of 80 kg and a density of 955 kg/m3 (excluding the air in his lungs). (a) Calculate his volume. (b) Find the buoyant force air exerts on him. (c) What is the ratio of the buoyant force to his weight?
A container of water has a cross-sectional area of A=0.1m2 . A piston sits top of the water (see be following figure). There is a spout located 0.15 m from the bottom of tank, open to the atmosphere, and a stream of water exits the spout. The cross sectional area of the spat is As=7.0104m2 . (a) What is the velocity of the water as it leaves the spout? (b) If the opening of the spout is located 1.5 m above the grand, how far from be pout does water hit the floor? Ignore friction and dissipative forces.

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