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3-m-high large tank is initially filled with water. The tank water surface is open to the atmosphere, and a sharp-edged 10-cm-diameter orifice at the bottom drains to the atmosphere through a horizontal 80-m-long pipe. If the total irreversible head loss of the system is determined to be 1.5 m, determine the initial velocity of the water from the tank. Disregard the effect of the kinetic energy correction factors.

Respuesta :

Answer:

The initial velocity of the water from the tank is 5.42 m/s

Explanation:

By applying Bernoulli equation between  point 1 and 2

[tex]\dfrac{P_1}{\rho g}+\dfrac{V_1^2}{2g}+Z_1=\dfrac{P_2}{\rho g}+\dfrac{V_2^2}{2g}+Z_2+h_L[/tex]

At the point 1

P₁=0  ( Gauge pressure)

V₁= 0 m/s

Z₁=3 m

At point 2

P₂=0  ( Gauge pressure)

Z₂= 0 m/s

[tex]h_L=1.5\ m[/tex]

Now by putting the values

[tex]\dfrac{P_1}{\rho g}+\dfrac{V_1^2}{2g}+Z_1=\dfrac{P_2}{\rho g}+\dfrac{V_2^2}{2g}+Z_2+h_L[/tex]

[tex]Z_1-h_L=\dfrac{V_2^2}{2g}[/tex]

[tex]3-1.5=\dfrac{V_2^2}{2\times 9.81}[/tex]

[tex]V_2=\sqrt{2\times 1.5\times 9.81}\ m/s[/tex]

V₂= 5.42 m/s

The initial velocity of the water from the tank is 5.42 m/s

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