Question

Consider the Ballard Locks as shown below. When traveling from the lake to the bay, there is a difference in
height of an average of 21 feet. The high side is the fresh water side. The locks allow boats traveling from fresh water to be lowered gently in an enclosed ‘lock’ down to the level of the salt water in the bay. A boat enters the locks through double entry gates on the fresh water (right) side. The entry gates are closed and with both sets of gates closed, water flows from the fresh water side to salt water side, until the water levels are equal. It takes 10 minutes to go from the height of the lake to that of the bay. Then the exit gates (left) are opened to let the boats pass to the Puget sound. The height of the fresh water is hfw = 50 feet in depth, the width of the lock is w=30 ft, the length is L =80 ft. The gates are of equal length and meet at the centerline of the lock at an angle theta =20 degrees. The rough concrete pipes that connect the salt and fresh sides are at the bottom of the locks, have an unknown diameter, and have three sections with lengths Lpy = 10 ft and Lpx = 30 ft. The sections are connected with smooth 90 degree bends with R/d = 5.

entry gates exit gates fw fresh salt fresh Side viewalt pipe exit gates ?_L_ ? Top view fresh pipe

Find:

(a) Find the force and torque on the individual exit gates when the boat enters the lock and the water levels are at a
maximum height difference.

(b) Use this information to describe why the gates are designed to close at the angle theta.

(c) Assuming the flow has no losses, provide the equation for the flow rate between the salt and fresh water sides.

(d) What diameter pipe should be used to connect the fresh and salt water sides?

(e) What is the maximum flow rate for this system?

(f) If you account for the fact that the water is viscous, how much would this maximum flow rate decrease? You
should assume that the pipes are rough concrete and end flush with the walls of the locks. How big of a pipe
would you need to obtain the maximum velocity you obtained when you assumed the flow was inviscid?

(g) What is the force and torque on the exit gate when the water levels are equal?

Answer 1

average height is 21 feet. Time taken from height to lake is 10 mins. Fresh water height is 50 feet width of the lock is 30 feet Length is 80 feet angle is theta = 20 degree Lengths are LP_x = 30 ft and LP_y = 10 ft Connected with 90 degree bends with R/d = 5. Force and Torque on the individual gates when the boat enters the lock and water level are at a maximum height difference Considering the given values, volume is l times b times h \r\n V = 80 times 50 times 30 = 4000 times 30 = 120000 Area = l times b = 80 times 80 = 4000 R = rho hh A + 2 F_s sin alpha The forces F_s is given as, R = A rho gh + rho gWh^2 tan theta Hence, force = A - h^2 tan theta force = 4000 - (50) ^2 tan(30)