Respuesta :
Answer:
W = - 523.425 W = -0.5234 kW
Negative sign show power input to the pump
Explanation:
By using energy balanced at state q and state 2
[tex]\dot m ( h_1 +\frac{v_1^2}{2} + gz_1) + Q = \dot m ( h_2 +\frac{v_2^2}{2} + gz_2) + w[/tex]
As it is given neglect kinetic energy and heat transfer therefore above equation rduece to
[tex]\dot m ( h_1 + gz_1) = \dot m ( h_2 + gz_2) + W[/tex]
[tex]W = \dot m ( h_1-h_2) + \dot m g (z_1 - Z_2)[/tex]
As temp remain cosntant , so enthalapy difference is givena s
[tex]h_1 -h_2 = v_f (p_1 - p_2)[/tex]
from saturated water tables, for temperature 15 degree celcius specific volume of water is
[tex]v_1 =v_f = 1.009 \times 10^{-3} m^3/kg[/tex]
[tex]W = \dot m ( h_1-h_2) + \dot m g (z_1 - Z_2)[/tex]
[tex]W = \dot m v_f (p_1 - p_2)+ \dot m g (z_1 - Z_2)[/tex]
putting zi =0, z2 = 15, m= 1.5 kg/s
[tex]W = 1.5\times 1.009\times 10^[-3} (1-3) \times 10^5 + 1.5\times 9.81\times(0-15)[/tex]
W = - 523.425 W
Negative sign show power input to the pump
The required power by the pump will be "-523.425 W".
Power and Temperature
According to the question,
Mass flow rate, m = 1.5 kg/s
Outlet temperature, z₂ = 15°C
By using energy balanced,
→ m(h₁ + [tex]\frac{v_1^2}{2}[/tex] + gz₁) + Q = m(h₂ + [tex]\frac{v_2^2}{2}[/tex] + gz₂) + w
By neglecting Kinetic energy, we get
m(h₁ + gz₁) + Q = m(h₂ + gz₂) + w
w = m(h₁ - h₂) + mg(z₁ - z₂)
Now, the enthalpy difference be:
h₁ - h₂ = [tex]v_f[/tex] (p₁ - p₂)
We know,
v₁ = [tex]v_f[/tex]
= 1.009 × 10⁻³ m³/kg
Now,
→ w = m[tex]v_f[/tex](p₁ - p₂) + mg(p₁ - p₂)
By substituting the values,
= 1.5 × 1.009 × 10⁻³ (1 - 3) × 10⁵ + 1.5 × 9.81 × (0.15)
= -523.425 W (Power input)
Thus the above response is correct.
Find out more information about power here:
https://brainly.com/question/24858512
