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rjkz [21]
2 years ago
14

In an incompressible three-dimensional flow field, the velocity components are given by u = ax + byz; υ = cy + dxz. Determine th

e form of the z component of velocity. If the z component were not a function of x or y what would be the form be?
Physics
1 answer:
Ksivusya [100]2 years ago
8 0

An incompressible flow field F in a 3D cartesian grid with components u,v,w:

F = u + v + w

where u,v,w are functions of x,y,z

Must satisfy:

∇·F = du/dx + dv/dy + dw/dz = 0

We have a field F defined:

F = u+v+w, u = ax+byz, v = cy+dxz

du/dx = a, dv/dy = c

Recall ∇·F = 0:

∇·F = du/dx + dv/dy + dw/dz = 0

a + c + dw/dz = 0

dw/dz = -a-c

Solve for w by separation of variables:

w = ∫(-a-c)dz

w = -az - cz + f(x,y)

f(x,y) is some undetermined function of x and y

The question states that w is not a function of x and y, therefore f(x,y) = 0...

w = -az - cz

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3 years ago
A 0.100-kg ball traveling horizontally on a frictionless surface approaches a very massive stone at 20.0 m/s perpendicular to wa
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Answer:

Change in momentum of the stone is 3.673 kg.m/s.

Explanation:

Given:

Mass of the ball on the horizontal the surface, m = 0.10 kg

Velocity of the ball with which it hits the stone, v = 20 m/s

According to the question it rebounds with 70% of the initial kinetic energy.

We have to find the change in momentum i.e Δp

Before that:

We have to calculate the rebound velocity with which the object rebounds.

Lets say that the rebound velocity be "v1" and KE remaining after the object rebounds be "KE1".

⇒ KE_1=0.7\times \frac{mv^2}{2}    

⇒ KE_1=0.7\times \frac{0.10\times (20)^2}{2}

⇒ KE_1=0.7\times \frac{0.10\times 400}{2}

⇒ KE_1=14 Joules (J).

Rebound velocity "v1".

⇒ KE_1=\frac{m(v_1)^2}{2}

⇒ v_1 = \sqrt{\frac{2KE_1}{m} }

⇒ v_1 = \sqrt{\frac{2\times 14}{0.10} }

⇒ v_1=16.73

⇒ v_1=-16.73 m/s ...as it rebounds.

Change in momentum Δp.

⇒ \triangle p= m\triangle v

⇒ \triangle p= 0.10\times (20-(-16.73)

⇒ \triangle p= 0.10\times (20+16.73)

⇒ \triangle p= 0.10\times (36.73)

⇒ \triangle p = 3.673 Kg.m/s

The magnitude of the change in momentum of the stone is 3.673 kg.m/s.

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3 years ago
Which statements describe a closed circuit? Check all that apply. Bulbs will shine. Bulbs will not shine. The circuit is incompl
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3 years ago
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Verify that for values of n less than 8, the system goes to a stable equilibrium, but as n passes 8, the equilibrium point becom
irakobra [83]

Answer:

Biological system is one of the major causes of oscillation due to sensitive negative feedback loops. For instance, imagine a father teaching his son how to drive, the teen is trying to keep the car in the centre lane and his father tell him to go right or go left as the case may be. This is a example of a negative feedback loop of a biological system. If the father's sensitivity to the car's position on the road is reasonable, the car will travel in a fairly straight line down the centre of the road. On the other hand, what happens if the father raise his voice at the son "go right" or when the car drifts a bit to the left? The startled the son will over correct, taking the car too far to the right. The father will then starts yelling "go left" then the boy will over correct again and the car will definitely oscillate back and forth. A scenario that indicates the behavior of a car driver under a very steep feedback control mechanism. Since the driver over corrects in each direction. Therefore causes oscillations.

Explanation:

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3 years ago
A skydiver falls out of a plane from rest, and experiences no air resistance. Eventually, this skydiver reaches a velocity of 33
shusha [124]

Answer:

the time taken for the motion is 3.37 s

Explanation:

Given;

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final velocity of the skydiver, v = 33 m/s

The time taken for the motion is calculated as;

v = u + gt

33 = 0 + 9.8t

33 = 9.8t

t = 33 / 9.8

t = 3.37 s

Therefore, the time taken for the motion is 3.37 s

3 0
3 years ago
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