Question

1. One of the fundamental equations in fluid flow is the equation of discontinuity.
A. True
B. False

2. What is the equation for conservation of flow rate of an incompressible fluid through various cross sections of tube? This fluid has a speed of $v_1$ through a cross section $A_1$ and the speed of $v_2$ through a cross section $A_2$ .
A. $v_1A_1=v_2A_2$
B. $v_2A_1=v_1A_2$

3. Now there is water running through a tube with two cross sections, $A_1$ =2 meter^2 and $A_2$ = 5 meter^2. Known that the speed $v_1$ at cross section $A_1$ is 1 meter/second, what is the value of $v_2$ ?
A. $\frac{5}{2} m/s$
B. $\frac{2}{5} m/s$

4. We have the Bernoulli equation, $p_1 + \frac{\rho}{2} v_1^2=p_2+\frac{\rho}{2}v_2^2$ where $p_1$ is the pressure when the fluid has the speed of $v_1$ through across section $A_1$ and $p_2$ is the pressure when the fluid has the speed of $v_2$ through across section $A_2$ , $\rho$ is the density.

We used the equation for conservation of energy for an incompressible fluid in the tube to get Bernoulli euqation. What is the equation conservation of energy in this case? Hint: $p_1V_1$ is a part of energy stored in the system when the fluid has the speed of $v_1$ through across section $A_1$ and kinetic energy is the other part of this energy.( $E_{k_1}=\frac{1}{2}m_1v_1^2$ where $m_1=\rho V_1$ ). $p_2V_2$ is a part of energy stored in the system when the fluid has the speed of $v_2$ through across section $A_2$ and kinetic energy is the other part of this energy.( $E_{k_2}=\frac{1}{2}m_2v_2^2$ where $m_2=\rho V_2$ )

A. $p_1V_1+\frac{1}{2}m_2v_2^2=p_2V_2+\frac{1}{2}m_1v_1^2$
B. $p_1V_1+\frac{1}{2}m_1v_1^2=p_2V_2+\frac{1}{2}m_2v_2^2$

5. Now there is water running through a tube with two cross sections, $A_1$ 0.2 meter^2 and $A_2$ = 0.4 meter^2, there is a pressure difference $\Delta p_{1,2}=p_2-p_1=$ 15 Pa. What is value of the speed $v_2$ at cross section $A_2$ ? Water density is 1000 kg/meters^3. Hint: you can Bernoulli equation, $p_1 + \frac{\rho}{2} v_1^2=p_2+\frac{\rho}{2}v_2^2$ .

A. $\sqrt{10}$ m/s
B. 0.01 m/s
C. 1 m/s
D. 0.1 m/s

Answer 1

1. One of the fundamental equations in fluid flow is the equation of discontinuity.
B. False

It is the equation of continuity

2.
A. $v_1A_1=v_2A_2$

3) As we know

$v_1A_1=v_2A_2$

1*2 = v2*5

v2 = 2/5 m/s


4 )

B.    $p_1V_1+\frac{1}{2}m_1v_1^2=p_2V_2+\frac{1}{2}m_2v_2^2$

5. Last option is correct
D. 0.1 m/s