A D 0 = 1 2-rn-diameter tank is initially filled with water 2 m above the center of a D = 1 0-cm- diameter valve near the bottom. The tank surface is open to the atmosphere. and the tank drains through a L = 95-m-long pipe connected to the valve. The friction factor of the pipe is given to bef 0.0 15, and the discharge velocity is expressed as V = 2 g z 1.5 + f L / D where z is the water height above the center of the valve. Detenuine ( a ) the initial discharge velocity from the tank and (b) the time required to empty the tank. The tank can be considered to be empty when the water level drops to the center of the valve.
A D 0 = 1 2-rn-diameter tank is initially filled with water 2 m above the center of a D = 1 0-cm- diameter valve near the bottom. The tank surface is open to the atmosphere. and the tank drains through a L = 95-m-long pipe connected to the valve. The friction factor of the pipe is given to bef 0.0 15, and the discharge velocity is expressed as V = 2 g z 1.5 + f L / D where z is the water height above the center of the valve. Detenuine ( a ) the initial discharge velocity from the tank and (b) the time required to empty the tank. The tank can be considered to be empty when the water level drops to the center of the valve.
Solution Summary: The following figure shows the systematic diagram of discharge tank.
A D0= 1 2-rn-diameter tank is initially filled with water 2 m above the center of a D = 1 0-cm- diameter valve near the bottom. The tank surface is open to the atmosphere. and the tank drains through a L= 95-m-long pipe connected to the valve. The friction factor of the pipe is given to bef 0.0 15, and the discharge velocity is expressed as
V
=
2
g
z
1.5
+
f
L
/
D
where z is the water height above the center of the valve. Detenuine (a) the initial discharge velocity from the tank and (b) the time required to empty the tank. The tank can be considered to be empty when the water level drops to the center of the valve.
4. The figure below shows a bent pipe with the external loading FA
228 lb, and M₁ = M₂ = 1 kip-ft. The force Fernal loading FA = 300 lb, FB:
parallel to the y-axis, and
and yc = 60°.
= 125 lb, Fc
=
acts parallel to the x-z plane, the force FB acts
Cartesian resultan Coordinate direction angles of Fc are ac = 120°, ẞc = 45°,
a. Compute the resultant force vector of the given external loading and express it in
EST
form.
b. Compute the resultant moment vector of the given external loading about the origin, O,
and express it in Cartesian vector form. Use the vector method while computing the
moments of forces.
c. Compute the resultant moment vector of the given external loading about the line OA
and express it in Cartesian vector form.
:00 PM EST
k
ghoufran@buffaternal du
2 ft
M₁
A
40°
FA
M2
C
18 in
1 ft
Fc
25
houfran@bald.edu - Feb 19,
3 ft
FB
The differential equation of a cruise control system is provided by the following equation:
Find the closed loop transfer function with respect to the reference velocity (vr) .
a. Find the poles of the closed loop transfer function for different values of K. How does the poles move as you change K?
b. Find the step response for different values of K and plot in MATLAB. What can you observe?
c. For the given transfer function, find tp, ts, tr, Mp . Plot the resulting step response. G(s) = 40/(s^2 + 4s + 40)
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Perform the partial fraction expansion of the following transfer function and find the impulse response:
G(s) = (s/2 + 5/3) / (s^2 + 4s + 6)
G(s) =( 6s^2 + 50) / (s+3)(s^2 +4)
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