Question 4.8: Water at 20^◦ C flows at a uniform depth of 1.7 m in a recta...

(a) Assume that the fluid is momentarily brought to a stop at the downstream point 2, where \upsilon _{2}= 0 . Then, in order to determine the ideal velocity at point 1, the Bernoulli equation is applied between points 1 and 2. Furthermore, in order to determine the ideal flowrate in the channel, the continuity equation is applied at point 1 as follows:

b: = 4 m                 y: = 1.7 m                 A: = b. y= 6.8 m^{2}                 v_{2}: = 0 \frac{m}{sec}

h_{1}: = 1.5 m                  h_{2}: = 1.75 m                  z_{1}: = 0 m                  z_{2}: = 0 m

\rho : = 998 \frac{kg}{m^{3}}                  g: = 9.81 \frac{m}{sec^{2}}                 \gamma : = \rho .g = 9.79 \times 10^{3} \frac{kg}{m^{2}s^{2}}
p_{1}: = \gamma . h_{1}= 1.469 \times 10^{4} \frac{N}{m^{2}}                                   p_{2}: = \gamma . h_{2}= 1.713 \times 10^{4} \frac{N}{m^{2}}

Guess value:                   v_{1}= 1 \frac{m}{sec}                  Q= 1 \frac{m^{3}}{sec}

Given

\frac{p_{1} }{\gamma } + z_{1} + \frac{v^{2}_{1} }{2.g} = \frac{p_{2} }{\gamma } + z_{1} + \frac{v^{2}_{2} }{2.g} Q = v_{1}
\left ( \begin{matrix} v_{1} \\ Q \end{matrix} \right ) : = Find (v_{1}, Q)

v_{1}= 2.215 \frac{m}{s}                            Q= 15.06 \frac{m^{3}}{s}

Application of the Bernoulli equation for the pitot tube illustrates a conversion of kinetic energy to pressure energy.
(b) The EGL and HGL are illustrated in Figure EP 4.8.