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Sergeeva-Olga [200]
3 years ago
10

Problem 3: Soil Classification using the AASHTO and USCS Systems

Engineering
1 answer:
nataly862011 [7]3 years ago
5 0

<u>Solution:</u>

Given\\                   \(\quad W=3000 Ib , \quad m=\frac{W}{g}=\frac{3000}{322} \ slug =93.1677 slug\)\\K_{e q}=2160 lbs / wp =2100 \frac{ lbs }{10} \frac{ x 12}{1 ft }=(2160 \times 12) lb / ft$$

a) The natural frequency

\begin{aligned}&\left(\omega_{n}\right)=\sqrt{\frac{K_{e q}}{m}}\\&=\sqrt{\frac{2160 \times 12}{93.1677}}\\&\omega_{n}=16.68 \text { rad } | s\\&\omega_{n}=\frac{2 \pi}{T}\\&16.68=\frac{2 \pi}{T}\\&T=0.3767 s\end{aligned}

b)

Given, \(t=10 s , \quad y(t)=6 in = A\)\\\(y(t)=A \cos \left(\omega_{n} t+\phi\right) \rightarrow 0\)\\\(6=6 \cos (16.68 \times 10+\phi)\)\\\(1=\cos (166.8+\phi)\)\\\(166.8+\phi=0\)\\\phi=-166.8\)\\At \(t=0, \quad y(0)=6 \cos (16.68 \times 0-166.8)\) {y(0)}=-5.74 in

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The maximum volume flow rate of kerosene is 8.3 L/s

<h3>What is the maximum volume flow rate?</h3>

In fluid dynamics, the maximum volume flow rate (Q) is the volume or amount of fluid flowing via a required cross-sectional area per unit time.

In fluid mechanics, using the following relation, we can determine the maximum volume flow rate of kerosene.

  • Power = mass flow rate(m) × specific work(w)   --- (1)
  • Specific work = acceleration due to gravity (g) × head (h)   ---- (2)
  • Mass flow rate (m) = density (ρ) × volume flow rate (Q) --- (3)

By combining the three equations together, we have:

The power gained through the fluid pump to be:

  • P = ρ × Q × g × h

Making Q the subject, we have:

\mathbf{Q = \dfrac{P}{\rho \times g \times h}}

where:

  • P = 2 kW = 2000 W
  • ρ = 0.820 kg/L
  • g = 9.8 m/s
  • h = 30 m

\mathbf{Q = \dfrac{2000 \ W }{820 \ kg/m^3 \times 9.8 m/s \times 30 \ m}}

Q  = 0.008296 m³/s

Q ≅ 8.3 L/s

Learn more about the maximum volume flow rate here:

brainly.com/question/19091787

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Liquid flows at steady state at a rate of 2 lb/s through a pump, which operates to raise the elevation of the liquid 100 ft from
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Answer:

D) 1.04 Btu/s from the liquid to the surroundings.

Explanation:

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flow rate (m) = 2 lb/s

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liquid specific enthalpy at the exit (h_{2}=40.94 Btu/lb)

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final elevation (z_2=100ft)

acceleration due to gravity (g) = 32.174 ft/s²

W_{cv} = 3 Btu/s

The energy balance equation is given as:

Q_{cv}-W{cv}+m[(h_1-h_2)+(\frac{V_1^2-V_2^2}{2})+g(z_1-z_2)]=0

Since  kinetic energy effects are negligible, the equation becomes:

Q_{cv}-W{cv}+m[(h_1-h_2)+g(z_1-z_2)]=0

Substituting values:

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Explanation:

A solid state laser contains a cavity like structure fitted with spherical mirrors or plane mirrors at the end filled with a rigidly bonded crystal. It uses solid as the medium. It uses glass or crystalline materials.

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