Fluid Mechanics( tank drainage)

Question 1

How do you determine the time it takes to completely drain a tank with uniform cross-sectional area?

Answer 1

t= a0 * Cd/A * sqrt(2H(0)/g)

Question 2

Determine a function describing the square root of height of water as a function of time

( tank drainage with uniform cross-sectional area)

Answer 2

sqrt(H(t))= sqrt(H0) - a0 * Cd/A * sqrt(g/2) * t

Question 3

what is the Cd value?

Answer 3

Orifice Coefficient:

• effects the drainage of the tank
• arises from converging streamlines
• Varies with orifice type and shape of diameter
• ( each orifice different=> best obtained by experiment) =>empirical value!

Question 4

Name some typical Cd values (orifice forms)

Answer 4

• short tube up: Cd=0.5
• short tube down: Cd=0.8
• sharp:Cd=0.6
• rounded: Cd=1

Question 5

what is a dynamical system?

Answer 5

best approach found: can be described using a mathematical equation dhdt=…

ODE can be used to solve equations describing dynamical systems

two variables, one changes over time

involves velocety, force, acceleration and displacement

Question 6

What is an ODE

Answer 6

ordinary differential equation

single variable

used to solve dynamical systems