mekflu

Soal No. 1
Ahmad mengisi ember yang memiliki kapasitas 20 liter dengan air dari sebuah kran seperti gambar berikut! 

Jika luas penampang kran dengan diameter D₂ adalah 2 cm² dan kecepatan aliran air

di kran adalah 10 m/s tentukan:
a) Debit air
b) Waktu yang diperlukan untuk mengisi ember

Pembahasan
Data :
A₂ = 2 cm² = 2 x 10⁻⁴ m²
v₂ = 10 m/s
a) Debit air
Q = A₂v₂ = (2 x 10⁻⁴)(10)
Q = 2 x 10⁻³ m³/s
b) Waktu yang diperlukan untuk mengisi ember
Data :
V = 20 liter = 20 x 10⁻³ m³
Q = 2 x 10⁻³ m³/s
t = V / Q 

t = ( 20 x 10⁻³ m³)/(2 x 10⁻³ m³/s )
t = 10 sekon

Soal No. 2
Pipa saluran air bawah tanah memiliki bentuk seperti gambar berikut! 

Jika luas penampang pipa besar adalah 5 m² , luas penampang pipa kecil adalah 2 m² dan kecepatan aliran air pada pipa besar adalah 15 m/s, tentukan kecepatan air saat mengalir pada pipa kecil!

Pembahasan
Persamaan kontinuitas
A₁v₁ = A₂v₂
(5)(15) = (2)v₂
v₂ = 37,5 m/s

4. Sebuah pipa 150 mm mengalirkan 0.08 m³/s, pipa itu bercabang menjadi dua pipa yang satu garis tengahnya 50 mm dan yang lain garis tengahnya 100 mm. Jika kecepatan dalam pipa 50 mm besarnya 12 m/det, berapakah kecepatan dalam pipa 100 mm ?

Pembahasan :

Dik :

d_B : 50 mm = 0,05 m

d_C : 100 mm = 0,1 m

υ_B : 12 m/s

Q_A : 0,08 m³/s

Dit : υ_C ... ?

Jawab :

Q_A = Q_B + Q_C

Q_A = ¼ π d_b² υ_b + ¼ π d_c² υ_C

0,08 m³/s = ¼ (3,14) (0,05 m)² (12 m/s) + ¼ (3,14) (0,1 m)² υ_C

0,08 m³/s = 0,02355 m³/s + 0,00785 m² υ_C

0,00785 m² υ_C = 0,05645 m³/s

υ_C = 7,2 m/s

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SIKLUS DIESEL

SIKLUSDIESEL

In Max's senior capstone design, the thermal efficiencies and the compression ratios of an ideal Otto cycle and an ideal Diesel cycle are required.

Assumptions:

• Cold-air-standard assumption is valid for this analysis. The constant volume specific heat c_v = 0.718 kJ/(kg-K), the constant pressur specific heat c_P = 1.005 kJ/(kg-K)
• Model the cycle in the car engine as an ideal Otto cycle and an ideal Diesel cycle, respectively.

     

P-v and T-s Diagram of the Otto Cycle

 

(1) Determine the thermal efficiency and compression ratio using ideal Otto-cycle model

The P-v and T-s diagrams of the ideal Otto cycle are shown on the left. The thermal efficiency and compression ratio using the Otto-cycle model has been determined in the previous section. They are:

      Thermal efficiency: η_{th, Otto} = 53.3%

      Compression ratio: r = 6.7

     

P-v and T-s Diagram of the Diesel Cycle

 

(2) Determine the thermal efficiency and compression ratio using Diesel-cycle model

The P-v and T-s diagrams of the ideal Diesel cycle are shown on the left. The previous section, the properties at the four states of an Otto cycle was determined. They are:

      state 1: T₁ = 15^oC, P₁ = 100 kPa (given)
      State 2: T₂ = 343.3^oC
      State 3: T₃ = 1800^oC (given)
      State 4: T₄ = 695.7^oC

The heat input to the cycle is:

      q_in,Otto = c_v23 (T₃ - T₂) = 0.718(1800 - 343.3)
                 = 1045.9 kJ

In Diesel cycle, with the temperature limit is the same as In Otto cycle, temperature at state 1 and state 3 are:

      T₁ = 15^oC
      T₃ = 1800^oC

Also, heat input is the same as in the ideal Otto cycle. In Diesel cycle, heat is input from the constant pressure cycle.

      q_in,Diesel = c_P23 (T₃ - T₂) = 1.005 (1800 - T₂)
                   = 1045.9 kJ

The temperature at state 2 can be determined from the above expression. That is,

      T₂ = 759.3^oC = 1032.3 K

The thermal efficiency of the ideal Diesel cycle is:

     

where r is the compression ratio and r_c is the cutoff ratio.

      r = v₁/v₂
      r_c = v₃/v₂

In Diesel cycle, process 1-2 is isentropic compression process. It gives,

     

Hence, the compression ratio of an ideal Diesel-cycle is 24.3, which is much higher than the compression ratio of an ideal Otto-cycle, which is 6.7.

Process 2-3 in an ideal Diesel cycle is an constant pressure cycle. Thus,

     

It gives that the cutoff ratio equals 2.01.

Substitute the compression ratio and cutoff ratio to the expression of thermal efficiency yields,

     

Also, the thermal efficiency of the ideal Diesel-cycle is much higher than the ideal Otto-cycle, which is 53.3%.

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SIKLUS OTTO

	In Max's senior capstone design, the thermal efficiencies and the compression ratios of an ideal Otto cycle and an ideal Diesel cycle are required. Assumptions: Cold-air-standard assumption is valid for this analysis. The constant volume specific heat cv = 0.718 kJ/(kg-K), the constant pressur specific heat cP = 1.005 kJ/(kg-K) Model the cycle in the car engine as an ideal Otto cycle and an ideal Diesel cycle, respectively.
P-v and T-s Diagram of the Otto Cycle		(1) Determine the thermal efficiency and compression ratio using ideal Otto-cycle model The P-v and T-s diagrams of the ideal Otto cycle are shown on the left. The thermal efficiency and compression ratio using the Otto-cycle model has been determined in the previous section. They are:       Thermal efficiency: ηth, Otto = 53.3%       Compression ratio: r = 6.7
P-v and T-s Diagram of the Diesel Cycle		(2) Determine the thermal efficiency and compression ratio using Diesel-cycle model The P-v and T-s diagrams of the ideal Diesel cycle are shown on the left. The previous section, the properties at the four states of an Otto cycle was determined. They are:       state 1: T1 = 15oC, P1 = 100 kPa (given)       State 2: T2 = 343.3oC       State 3: T3 = 1800oC (given)       State 4: T4 = 695.7oC The heat input to the cycle is:       qin,Otto = cv23 (T3 - T2) = 0.718(1800 - 343.3)                  = 1045.9 kJ In Diesel cycle, with the temperature limit is the same as In Otto cycle, temperature at state 1 and state 3 are:       T1 = 15oC       T3 = 1800oC Also, heat input is the same as in the ideal Otto cycle. In Diesel cycle, heat is input from the constant pressure cycle.       qin,Diesel = cP23 (T3 - T2) = 1.005 (1800 - T2)                    = 1045.9 kJ The temperature at state 2 can be determined from the above expression. That is,       T2 = 759.3oC = 1032.3 K The thermal efficiency of the ideal Diesel cycle is:        where r is the compression ratio and rc is the cutoff ratio.       r = v1/v2       rc = v3/v2 In Diesel cycle, process 1-2 is isentropic compression process. It gives,        Hence, the compression ratio of an ideal Diesel-cycle is 24.3, which is much higher than the compression ratio of an ideal Otto-cycle, which is 6.7. Process 2-3 in an ideal Diesel cycle is an constant pressure cycle. Thus,        It gives that the cutoff ratio equals 2.01. Substitute the compression ratio and cutoff ratio to the expression of thermal efficiency yields,        Also, the thermal efficiency of the ideal Diesel-cycle is much higher than the ideal Otto-cycle, which is 53.3%.

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