# Fluid Mechanics Question -- fluid on block?

• oobgular
In summary, the problem involves finding the flow rate needed to tip a block with dimensions of 0.015 x 0.2 x 0.1 meters and weight of 6 Newtons, when a 15mm-diameter jet of water is deflected by the block. The equations used are mass conservation and momentum conservation. In order to find the required flow rate, the moment of the water jet impact must be equal to the moment of the centroid of block mass. The dynamic force due to impact of a flow may be proportional to half the flow rate, density, and velocity squared. To solve the problem, one must consider the x component of momentum of the fluid before and after it contacts the block and spreads along the surface
oobgular

## Homework Statement

A block has dimensions 0.015 x 0.2 x 0.1 meters and weighs 6 Newtons. A 15mm-diameter jet of water is deflected by the block. Find the flow rate needed to tip the block.

## Homework Equations

Mass conservation: ∂/∂t ∫(control volume)ρ d∀ + ∫(control surface) ρv•n dA = 0
Momentum conservation: ∂/∂t ∫(control volume)ρv d∀ + ∫(control surface) ρv(v•n) dA = ∫(control surface) p*ndA + Viscous forces + ∫(control volume)ρgd∀

## The Attempt at a Solution

I know this is steady state, so the first term in each equation (time derivative of mass in the control volume) is zero. I am trying to use a control volume that follows the streamlines, to make the surface integrals easier. However, I don't know what area to use as the output, or even how to approach finding it. Also, how should I relate the force on the block to the force required to tip the block? I assume it has to do with a Moment balance, but I'm not sure how to do that.

I don't want you to solve the problem for me, just some direction would be nice. Thanks!

The centre of mass of the block must be pushed above the right hand side edge of the base before the block will fall freely. Getting the block to start tipping will be the critical force.

As the block starts to tip, the moment of the water jet impact about the RHS base edge will be equal to the moment of the centroid of block mass about the same edge.

If I remember rightly, the dynamic force due to impact of a flow will be proportional to half the flow rate * density * velocity squared. You had better check that by application of conservation laws to the flow path of the fluid.

What is the x component of momentum of the fluid flowing upward and downward along the block along the contact area? How much x momentum does the fluid have after it contacts the block and spreads along the surface? What control volume can you use?

## 1. What is fluid mechanics?

Fluid mechanics is the branch of physics that studies the behavior of fluids, such as liquids and gases, when they are in motion or at rest. It involves studying how forces and pressure affect the movement and properties of fluids.

## 2. What is the difference between a liquid and a gas in fluid mechanics?

Liquids and gases are both considered fluids in fluid mechanics, but they have different properties. Liquids are generally more dense and have a defined volume, while gases are less dense and can change volume easily.

## 3. How does fluid pressure affect the block in this scenario?

In this scenario, the fluid pressure will exert a force on the block, causing it to move or remain at rest depending on the direction and magnitude of the force. The pressure is determined by the density of the fluid and the depth of the block.

## 4. What is Bernoulli's principle and how does it relate to this question?

Bernoulli's principle states that as the speed of a fluid increases, the pressure decreases. In this question, the fluid on the block is moving, so Bernoulli's principle applies and the pressure on the block will be lower on the side where the fluid is moving faster.

## 5. How can we calculate the force of the fluid on the block?

The force of the fluid on the block can be calculated using the equation F = PA, where P is the pressure exerted by the fluid and A is the surface area of the block. The pressure can be calculated using the formula P = ρgh, where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the block in the fluid.

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