Answered: Determine whether the given velocity…

Science

Physics

Determine whether the given velocity vector of a fluid is rotational/ irrotational F(х, у, 2) %3D (х, —у, z)

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...

See similar textbooks

Related questions

Q: A tube of length L is filled completely with an incompressible liquid of mass M and closed at both…

Q: What is the ratio of heights to which ethyl alcohol andwater are raised by capillary action in the…

A: The expression for the height to which the ethyl alcohol is raised in the capillary tube is given…

Q: A garden hose of inner radius 1.00 cm carries water at 3.13 m/s. The nozzle at the end has inner…

A: Given values - Inner radius of garden hose = r1 =1 cm =1×10-2 mInner radius of nozzle at the end…

Q: Under what conditions would a metal sphere dropping through a viscous liquid be in equilibrium?

Q: Oil (S=0.80) at 3000Pa flows at a constant rate of 1m³/s through the circular nozzle shown. What is…

A: To find out the net force exerted by the joint to hold the nozzle in place.

Q: A thin stream of water flows smoothly from a faucet and falls straight down. At one point, the water…

A: Given:density of the water, ρ = 1000 kg/m3at location 1velocity of the water, v1 = 1.07 m/sat…

Q: The differential change in pressure p close to the surface of a static fluid is given by the…

A: The differential change of pressure with respect to y is given by: dpdy=-3Ap2 Here, A is the…

Q: Given that the cylinder floats in water with its axis vertical. A steel anchor is attached to the…

Q: A hollow iron ball with a mass of 3 kg is floating in oil with density of 900 kg/cub.m. Density of…

A: Yes we can find by using Archimedes principle. As per this principle, Buoyant force=weight of…

Q: Calculate the Reynolds numbers for the flow of water through the following situations. You may…

A: Flow rate, Viscosity of water, Density of water, Radius of nozzle, Radius of hose,

Q: Once again, using our bicycle pump (same diameter) from question #9 and Figure 15-10, imagine that…

Q: Water flows through a cylindrical pipe of varying cross section. The velocity is 3.0 m/s at a point…

Q: For numbers 12 and 13, refer to the problem below. Water flows at a rate of 0.25 m3/min in a…

Q: The longitudinal stress developed in the thin spherical shells are (a) Perpendicular to the radial…

A: Wall thickness of a thin cylindrical and spherical shell will be equal or less than the 1/20 of the…

Q: A mixing beater consists of three thin rods, each 10.9 cm long. The rods diverge from a central hub,…

A: the drag force can be expressed as, R=12DρAv2=12DρArω2 1 v=rω the…

Q: A pipe with radius R narrows down to a radius R/2. If the speed of the fluid at the point with…

Q: A mixing beater consists of three thin rods, each 11.0 cm long. The rods diverge from a central hub,…

A: A) The power required to spin the beater can be found as, Here, τ and ω represent the net torque,…

Q: A small spherical bead of mass 3.00 g is released from rest at t =0 from a point under the surface…

A: (a) Write the given values of this problem. m=3 gvT=2 cm/sF=-kv

Q: A viscous liquid is present between two co- axial cylinders oflength 1, radii r, and r,. The inner…

A: When two coaxial cylinders rotate with angular velocity ωo and filled with viscous fluid, the force…

Q: The radius of a given capillary 0.0123 dm. A liquid whose density is 0.800 g/cc rises in this…

Q: Derive a relation for the capillary rise of a liquid between two large parallel plates a distance t…

Q: What should be the displacement of the liquid inside a capillary tube if its density and surface…

A: Since you have posted multiple question, we will solve the first one only as per the guideline.…

Q: Pressure is the same in every direction in a static fluid at a given depth True False

Q: Q.3. A battle ship weighs 127.53 MN. On filling the ship's boats on one side with water weighing…

Q: for accelaration flow the velocity for fluid is given : a=(3x^2+2yx)i+(2xy+2y)j determine…

A: Given:- for acceleration flow the velocity for fluid is given : a=(3x2+2yx)i+(2xy+2y)j Find:-…

Q: Water flows through a cylindrical pipe of varying cross section. The velocity is 3 m/s at a point…

A: We know that, F=v·Awhere,v is the flow velocity A is cross-sectional area and A=πr2, r being the…

Q: What volume of water is displaced by a submerged 2.0-kg cylinder made of solid aluminum? (aluminum…

A: Mass of solid aluminum cylinder is M = 2 kg Density of aluminium is d= 2.7 × 10³ kg/m³ Density of…

Q: Bowling balls are roughly the same size but come in a variety of weights. Given that the official…

Q: If the velocity profile of a fluid over a plate is parabolic with the vertex 20 cm from the plate,…

A: Given; Distance of vertex from plate= 20 [cm] Velocity at vertex= u= 120 [cm/s] Viscosity= μ= 8.5…

Q: If the net volume of fluid that passes through a surface per unit time in the positive direction is…

A: If the net volume of fluid that passes through a surface per unit time in the positive direction is…

Q: Please I want answer of this question. Many Thanks

A: The given values are,

Q: Calculate the Reynolds numbers for the flow of water through the following situations. You may…

A: Flow Rate (Q) = 0.5 L/s = 0.0005 m3/sViscosity (η) = 0.001005 Nm2-s

Q: Air that has amass density of 1.24 kg/m² (0.00241 slugs/ft) flows in a pipe with a diameter of 30 cm…

Q: Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm,…

Q: Pressure exerted anywhere in a confined compressible fluid is transmitted equally in all the…

Q: Pressure is the same in every direction in a static fluid at a given depth O True False

Q: Q5: A torque of 5 N.m is required to rotate the intermediate cylinder at 40 r/min. Calculate the…

A: As given, Length of all cylinder, L=500 mm=0.5 m Torque, τ=5 N·m Angular velocity, ω=40…

Q: Estimate the radius (mm) of a spherical particle of density 1789 kg/m³ that reaches a distance of…

A: Here given the viscosity and density of air are 1.923 × 10-⁵ kg/m.s and 1.301 kg/m³. The density of…

Q: When the fluid is said to be incompressible, which of the following parameters of the fluid remains…

A: Answer Option ( D - density ) If the fluid is incompressible, then it density will be constant.

Q: (1) 0.9 an angular velocity of 1 rad/sec about a stationary vertical axis 00' passing through end A.…

A: Given : An ideal fluid. Angular velocity of the tube, ω = 1 rad/sec Length of the tube, l = 10 m…

Q: ssm A patient recovering from surgery is being given fluid intravenously. The fluid has a density of…

A: The mass flow rate can be given by Qmass=mt=ρVt

Q: TSH Øtube 0 = 10 mm glass tube ↑ h mercury σ= 0.32 N m 20 mm

Q: n a flowing ideal fluid, the volume flow rate is _______." always constant sometimes…

A: Explanation: The rate of fluid flow through a particular area per unit time called flow rate, the…

Question

100%

Determine whether the given velocity vector of a fluid is rotational/ irrotational:
F(x,y,z) = (x,-y, z)
(х, —у, z)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Show that the Reynolds number NRis unitless by substituting units for all the quantities in its definition and cancelling.
A fluid flows through a horizontal pipe that widens, making a 45 angle with the y axis (Fig. P15.48). The thin part of the pipe has radius R, and the fluids speed in the thin part of the pipe is v0. The origin of the coordinate system is at the point where the pipe begins to widen. The pipes cross section is circular. a. Find an expression for the speed v(x) of the fluid as a function of position for x 0 b. Plot your result: v(x) versus x. FIGURE P15.48 (a) The continuity equation (Eq. 15.21) relates the cross-sectional area to the speed of the fluid traveling through the pipe. A0v0 = A(x)v(x) v(x)=A0v0A(x) The cross sectional area is the area of a circle whose radius is y(x). The widening pan of the pipe is a straight line with slope of 1 and intercept y(0) = R. y(x) = mx + b = x + R A(x) = [y(x)]2 = (x + R)2 Plug this into the formula for the velocity. Plug this into the formula for the velocity. v(x)=A0v0(x+R)2
The inside diameters of the larger portions of the horizontal pipe depicted in Figure P9.45 are 2.50 era. Water flows to the right at a rate of 1.80 104 m3/s. Determine the inside diameter of the constriction. Figure P9.45
The gravitational force exerted on a solid object is 5.00 N. When the object is suspended from a spring scale and submerged in water, the scale reads 3.50 N (Fig. P15.24). Find the density of the object. Figure P15.24 Problems 24 and 25.
Logs sometimes float vertically in a lake because one end has become water-logged and denser than the other. What is the average density of a uniform-diameter log that floats with 20.0% of its length above water?
A horizontal pipe 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter. If the pressure of the water in the larger pipe is 8.00 104 Pa and the pressure in the smaller pipe is 6.00 104 Pa, at what rate does water flow through the pipes?
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.
Q.3. A battle ship weighs 127.53 MN. On filling the ship's boats on one side with water weighing 588.6 kN and its mean distance from the centre of the ship being 10 m, the angle of displacement of the plumb line is 2° 16'. Determine the metacentric height.
A closed cylindrical vessel of diameter 15 cm and length 100 cm contains water up to a height of 80 cm. The vessel is rotated at speed of 500 rpm about its vertical axis. Find the speed of rotation of the vessel in rpm, when the axial depth is zero. a. 891.7 b. 645.23 c. 20.4 d. 56.06 With Free Body Diagram
A small spherical bead of mass 3.00 g is released from rest at t =0 from a point under the surface of a viscous fluid. The terminal speed is observed to be vT = 2.00 cm/s.Find a) the value of the constant k that appears in F = -kv, b) the time t at which the bead reaches 0.632 vT and c) the value of the resistive force when the bead reaches terminal speed.
A fuel pump sends gasoline form a car's fuel tank to the engine at a rate of 7.85 x 10-2 kg/s. The density of the gasoline is 736 kg/m3, and the radius of the fuel line is 3.62 x 10-3 m. What is the speed at which gasoline moves through the fuel line?
A child playing in the pool is using a cylindrical can as a boat for his toy soldiers. The can weighs 778.5 N with a height of 1.5 m and a diameter of (0.5)0.5 m. Which of the following most nearly gives the maximum number of toy soldiers, each weighing 1 kN, that the can could carry without sinking? a.) 6 b.) 9 c.) 5