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2 years ago

How do I prove that a = v * dv/dx?

1 answer:

6 0

Your book has applied the chain rule to produce:
dv/dt = dv/dx * dx/dt
Now, we can get dv/dx by:
1) Differentiate
x = vt, with respect to v.
dx/dv = t
Now, if we take the inverse of this, we can obtain dv/dx
dv/dx = 1/t
This is also proven by the fact that dv/dx is the change in velocity and if you multiply it by dv/dx, which is equivalent to dividing by the change in time, as we just proved, then you obtain acceleration.

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A fluid moves through a tube of length 1 meter and radius r=0.002±0.0002 meters under a pressure p=4⋅105±1750 pascals, at a rate

yaroslaw [1]

Answer:

The maximum error is $\Delta \eta = 2032.9$

Explanation:

From the question we are told that

The length is $l = 1\ m$

The radius is $r = 0.002 \pm 0.0002 \ m$

The pressure is $P = 4 *10^{5} \ \pm 1750$

The rate is $v = 0.5*10^{-9} \ m^3 /t$

The viscosity is $\eta = \frac{\pi}{8} * \frac{P * r^4}{v}$

The error in the viscosity is mathematically represented as

$\Delta \eta = | \frac{\delta \eta}{\delta P}| * \Delta P + |\frac{\delta \eta}{\delta r} |* \Delta r + |\frac{\delta \eta}{\delta v} |* \Delta v$

Where $\frac{\delta \eta }{\delta P} = \frac{\pi}{8} * \frac{r^4}{v}$

and $\frac{\delta \eta }{\delta r} = \frac{\pi}{8} * \frac{4* Pr^3}{v}$

and $\frac{\delta \eta }{\delta v} = - \frac{\pi}{8} * \frac{Pr^4}{v^2}$

$\Delta \eta = \frac{\pi}{8} [ |\frac{r^4}{v} | * \Delta P + | \frac{4 * P * r^3}{v} |* \Delta r + |-\frac{P* r^4}{v^2} |* \Delta v]$

substituting values

$\Delta \eta = \frac{\pi}{8} [ |\frac{(0.002)^4}{0.5*10^{-9}} | * 1750 + | \frac{4 * 4 *10^{5} * (0.002)^3}{0.5*10^{-9}} |* 0.0002 + |-\frac{ 4*10^{5}* (0.002)^4}{(0.5*10^{-9})^2} |* 0 ]$

$\Delta \eta = \frac{\pi}{8} [56 + 5120 ]$

$\Delta \eta = 647 \pi$

$\Delta \eta = 2032.9$

4 0

3 years ago

How do you find the voltage of a section of a parallel circuit?

sergiy2304 [10]

Answer: Voltage is the same across each component of the parallel circuit. The sum of the currents through each path is equal to the total current that flows from the source. You can find total resistance in a Parallel circuit with the following formula: 1/Rt = 1/R1 + 1/R2 + 1/R3 +.

Hope this helps!

3 0

3 years ago

A planet has a circular orbit around a star. It is a distance of 53,000,000 km from the centre of the star.

Kipish [7]

Answer:

it takes 365 days to revolve around the star(sun)

5 0

2 years ago

At standard temperature and pressure, carbon dioxide has a density of 1.98 kg/m3. What volume does 1.70 kg of carbon dioxide occ

nikitadnepr [17]

Answer:

<h2>volume= 0.85m^3</h2>

Explanation:

<em>The density of a substance is defined as the mass per unit volume of the substance, the unit is in kg/m^3 and it is represented by the greek letter rho</em>

Step one:

given data

we are told that the density of Co2= 1.98 kg/m3

and the mass of Co2 is= 1.70 kg

we know the relation between mass, volume and density is

$density=mass/volume$