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My name is Ann [436]
3 years ago
10

The velocity profile in fully developed laminar flow in a circular pipe of inner radius R 5 2 cm, in m/s, is given by u(r) 5 4(1

2 r2/R2). Determine the average and maximum velocities in the pipe and the volume flow rate.
Physics
1 answer:
xxMikexx [17]3 years ago
8 0

The question is not clear and the complete clear question is;

The velocity profile in fully developed laminar flow In a circular pipe of inner radius R = 2 cm, in m/s, is given By u(r) = 4(1 - r²/R²). Determine the average and maximum Velocities in the pipe and the volume flow rate.

Answer:

A) V_max = 4 m/s

B) V_avg = 2 m/s

C) Flow rate = 0.00251 m³/s

Explanation:

A) We are given that;

u(r) = 4(1 - (r²/R²))

To obtain the maximum velocity, let's apply the maximum condition for a single-variable continual real valued problem to obtain;

(d/dr)(u(r)) = 0

Thus,

(d/dr)•4(1 - (r²/R²)) = 0

4(d/dr)(1 - (r²/R²)) = 0

If we differentiate, we have;

4(0 - (2r/R²)) = 0

-8r/R² = 0

Thus, r = 0 and with that, the maximum velocity is at the centre of the pipe.

Thus, for maximum velocity, let's put 0 for r in the U(r) function.

Thus,

V_max = 4(1 - 0²/R²) = 4 - 0 = 4 m/s

B) Average velocity is given by;

V_avg = V_max/2

V_avg = 4/2 = 2 m/s

C) the flow can be calculated from;

Flow rate ΔV = A•V_avg

A is area = πr²

From question, r = 2cm = 0.02m

A = π x 0.02²

Hence,

ΔV = π x 0.02² x 2 = 0.00251 m³/s

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Answer:

The speed and direction of the apple is 1.448 m/s and 66.65°.

Explanation:

Given that,

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Suppose we find the final speed and direction of the apple in this case

Using conservation of momentum:

Before:

In x direction,

P_{b}=m_{p}v_{p}-m_{o}v_{o}

P_{b}=0.110\times1.13-0.150\times1.25

P_{b}=−0.0632\ kg-m/s

In y direction = 0

After:

v_{ay} is velocity of the apple in the y direction

v_{ax} is the velocity of the apple in the x direction

Momentum again:

In x direction,

0.110\times v_{ax}+0=−0.0632

v_{x}=\dfrac{−0.0632}{0.110}

v_{x}=−0.574\ m/s

In y-direction,

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v_{ay}=\dfrac{0.150\times0.977}{0.110}

v_{ay}=1.33\ m/s

We need to calculate the speed of apple

v_{a}=\sqrt{(v_{x})^2+(v_{y})^2}

Put the value into the formula

v_{a}=\sqrt{(−0.574)^2+(1.33)^2}

v_{a}=1.448\ m/s

We need to calculate the direction of the apple

Using formula of angle

\tan\theta=\dfrac{v_{ay}}{v_{ax}}

Put the value into the formula

\theta=\tan^{-1}(\dfrac{1.33}{0.574})

\theta=66.65^{\circ}

Hence, The speed and direction of the apple is 1.448 m/s and 66.65°.

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If you travel for three hours of a speed of 30 km/h, how far will you go?
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90km

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luda_lava [24]

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The best description looks like option D

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2 years ago
As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff ideal sprin
shepuryov [24]

Answer:

The magnitude of force must you apply to hold the platform in this position = 888.89 N

Explanation:

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The equation  for this  work done by the spring is expressed as:

W = \frac{1}{2}k_{eq}x^2

Making the spring constant k_{eq} the subject of the formula; we have:

k_{eq} = \frac{2W}{x^2}

Substituting our given values, we have:

k_{eq} = \frac{2*80}{0.180^2}

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The magnitude of the force that must be apply  to the hold platform in this position is given by the formula :

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adelina 88 [10]

Answer: On the basis of speed they are all equivalent.

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