How many Faces, Vertices and Edges are there on a cube?

By method of dimension show that the following equation are homogenous.

il63 [147K]

Answer:

Proof in explanataion

Explanation:

The basic dimensions are as follows:

MASS = M

LENGTH = L

TIME = T

i)

Given equation is:

$H = \frac{u^2Sin^2\phi}{2g}$

where,

H = height (meters)

u = speed (m/s)

g = acceleration due to gravity (m/s²)

Sin Ф = constant (no unit)

So there dimensions will be:

H = [L]

u = [LT⁻¹]

g = [LT⁻²]

Sin Ф = no dimension

Therefore,

$[L] = \frac{[LT^{-1}]^2}{[LT^{-2}]}\\\\\ [L] = [L^{(2-1)}T^{(-2+2)}]$

[L] = [L]

Hence, the equation is proven to be homogenous.

ii)

$F = \frac{Gm_1m_2}{r^2}\\\\$

where,

F = Force = Newton = kg.m/s² = [MLT⁻²]

G = Gravitational Constant = N.m²/kg² = (kg.m/s²)m²/kg² = m³/kg.s²

G = [M⁻¹L³T⁻²]

m₁ = m₂ = mass = kg = [M]

r = distance = m = [L]

Therefore,

$[MLT^{-2}] = \frac{[M^{-1}L^{3}T^{-2}][M][M]}{[L]^2}\\\\\ [MLT^{-2}] = [M^{(-1+1+1)}L^{(3-2)}T^{-2}]\\\\$

[MLT⁻²] = [MLT⁻²]

Hence, the equation is proven to be homogenous.

8 0

3 years ago

5. A stream of air at 12 bar and 900 K is mixed with another stream of air at 2 bar and 400 K with 2 times the mass flowrate. If

Softa [21]

Answer:

The anserrs to the question are

(a) The temperature would be 566.67 K and

(b) The pressure of the resulting air stream is 14 bar

Explanation:

Here the two streams of gases meet ad form a single stream

The steady-flow energy equation can be implemented at the mixing point of the to streams as follows

mₐhₐ₁ + mₙ hₙ₁ + Q° + W° = mₐhₐ₂ + mₙhₙ₂

Where the flow is adiabatic, we have

Q = 0 and W = 0 hence

mₐhₐ₁ + mₙ hₙ₁ = mₐhₐ₂ + mₙhₙ₂ where h = cp×T we have

mₐcpₐ×Tₐ + mₙcpₙ×Tₙ = mₐcpₐ×T + mₐcpₙ×T

Therefore the final temperature T is given by

$T = \frac{m_ac_{pa}T_a + m_nc_{pn}T_n}{m_ac_{pa} + m_nc_{pn}}$ for the same kind of gas cpₐ =cpₙ therefore

$T = \frac{m_aT_a + m_nT_n}{m_a + m_n}$ where mₐ and mₙ are mass flow rate

Therefore we have where Tₐ = = 900 K and Tₙ = 400 K and mₙ = 2mₐ gives

$T = \frac{m_a*900 + 2*m_a*400}{m_a + 2*m_a}$ = $T = \frac{900 + 800}{1 + 2}$ = 1700/3 = 566.67 K

From Dalton's law, the total pressure of a mixture of gases is equal to the sum of the partial pressures of the components of the mixture

Therefore the total pressure of the combined stream = pₐ + pₙ = p

= 12 bar + 2 bar = 14 bar

Stream pressure = 14 bar

4 0

3 years ago

Which formula is used to calculate average velocity?

Flauer [41]

Answer:

Explanation:

<h3>for average velocity we use this formula V Vavg =V1+V2÷2</h3>

5 0

4 years ago

What type of OS is very fast and small, and is often embedded, or built into the circuitry of a device?

Bezzdna [24]

Answer:

Real time operating system (RTOS)

Explanation:

Real time operating system is an operating system software which is used for the real-time applications that processes the data as soon as the input comes to the system.

It is very fast because it processes the data without any buffer delays.

In RTOS the scheduler provides a deterministic time which is predicted for the execution pattern. In a real-time operation the system must respond to each sequence of execution within a certain time frame which is the deadline for the operation so that the next inline process can be executed. Hence it is used in embedded systems and circuitry devices.

7 0

3 years ago

Suppose that a 1000 kg car is traveling at 25 m/s (aprox 55mph). Its brakes can apply a force of 5000N. What is the minimum dist

Brrunno [24]

Assuming the the car is travelling to the right (→):

$R(\rightarrow), F = ma$