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Chapter 6: Problem 85

Imagine a garden hose with a stream of water flowing out through a nozzle. Explain why the end of the hose may be unstable when held a half meter or so from the nozzle end.

Short Answer

Expert verified
The end of the hose may be unstable when held a half meter or so from the nozzle end due to the principles of inertia and unbalanced forces. The water flowing out of the hose creates a force, causing movement or instability. Furthermore, the farther the holding point from the nozzle, the more torque is applied to the hose, making it even more unstable.

Step by step solution

01

Understanding inertia

Inertia is the tendency of an object to resist changes in its state of motion. The hose as an object will try to stay at rest or maintain its movement unless acted upon by an external force. The flowing water out of the hose nozzle is exerting a force on the hose, thereby changing its state of motion.
02

Understanding unbalanced forces

When the forces on an object are unbalanced, the object will change its state of motion. In our case, the water flowing out of the hose creates an unbalance of forces which leads to the movement or instability of the hose.
03

Understanding the effect of the location where the hose is held

The further the hand reaches from the nozzle, the more torque or rotational force is applied to the hose. Torque is the force that causes rotation. When holding the hose closer to the nozzle, the hose is more stable because you are counteracting the force of the water closer to its source, reducing the amount of torque acting on the hose.

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Most popular questions from this chapter

A nozzle for an incompressible, inviscid fluid of density \(\rho=1000 \mathrm{kg} / \mathrm{m}^{3}\) consists of a converging section of pipe. At the inlet the diameter is \(D_{i}=100 \mathrm{mm},\) and at the outlet the diameter is \(D_{o}=20 \mathrm{mm} .\) The nozzle length is \(L=500 \mathrm{mm}\) and the diameter decreases linearly with distance \(x\) along the nozzle. Derive and plot the acceleration of a fluid particle, assuming uniform flow at each section, if the speed at the inlet is \(V_{i}=1 \mathrm{m} / \mathrm{s}\). Plot the pressure gradient through the nozzle, and find its maximum absolute value. If the pressure gradient must be no greater than \(5 \mathrm{MPa} / \mathrm{m}\) in absolute value, how long would the nozzle have to be?

Consider a two-dimensional fluid flow: \(u=a x+b y\) and \(v=c x+d y,\) where \(a, b, c\) and \(d\) are constant. If the flow is incompressible and irrotational, find the relationships among \(a, b, c,\) and \(d .\) Find the stream function and velocity potential function of this flow.

The \(\tan \mathrm{k},\) of diameter \(D,\) has a well-rounded nozzle with diameter \(d .\) At \(t=0,\) the water level is at height \(h_{0} .\) Develop an expression for dimensionless water height, \(h / h_{0},\) at any later time. For \(D / d=10,\) plot \(h / h_{0}\) as a function of time with \(h_{0}\) as a parameter for \(0.1 \leq h_{0} \leq 1 \mathrm{m} .\) For \(h_{0}=1 \mathrm{m},\) plot \(h / h_{0}\) as a function of time with \(D / d\) as a parameter for \(2 \leq D / d \leq 10\)

Consider the flow field with velocity given by \(\vec{V}=\left[A\left(y^{2}-x^{2}\right)-B x | \hat{i}+[2 A x y+B y] \hat{j}, A=1 \mathrm{ft}^{-1} \cdot \mathrm{s}^{-1}, B=1\right.\) \(\mathrm{ft}^{-1} \cdot \mathrm{s}^{-1} ;\) the coordinates are measured in feet. The density is \(2 \operatorname{slug} / \mathrm{ft}^{3},\) and gravity acts in the negative \(y\) direction. Calculate the acceleration of a fluid particle and the pressure gradient at point \((x, y)=(1,1)\)

Describe the pressure distribution on the exterior of a multistory building in a steady wind. Identify the locations of the maximum and minimum pressures on the outside of the building. Discuss the effect of these pressures on infiltration of outside air into the building.
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