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## Homework Statement

A pump is on a line. the data are:

P

_{1}=-0.4[bar]

[itex]\gamma[/itex]=0.8[itex]\cdot[/itex]10

^{4}[N/m

^{3}]

V

_{1}=3[m/s]

[tex]\frac{D_1}{D_2}=1.4[/tex]

H

_{P}=30[m] (head of pump)

See attached drawing.

## Homework Equations

Bernoulli equation:

[tex]H_1+\frac{V_1^2}{2g}+\frac{P_1}{\gamma}+H_P=H_2+ \frac{V_2^2}{2g} +\frac{P_2}{\gamma}[/tex]

## The Attempt at a Solution

The velocity after the pump:

[tex]V_2=V_1\frac{D_1^2}{D_2^2}=3\cdot 1.4^2=5.9[/tex]

Bernoulli equation:

[tex]\frac{-0.4\times10^5}{8000}+\frac{3^2}{20}+30=0.3+\frac{5.9^2}{20}+\frac{P_2}{\gamma}[/tex]

[tex]\Rightarrow\frac{P_2}{\gamma}=27.9 \Rightarrow P_2=2.2\times10^5[/tex]

The answer should be 1.87x10

^{5}[pa]