Depth and vertex angle of triangular channel for minimum perimeter

Problem
A triangular shaped channel is to be designed to carry 700 L/s on a slope of 0.0001. Determine what vertex angle and depth of water over the vertex will be necessary to give a section with minimum perimeter, assuming the channel is made of timber, n = 0.012. Use Manning’s formula.

A.   θ = 45°, h = 1.425 m C.   θ = 45°, h = 2.125 m
B.   θ = 90°, h = 2.215 m D.   θ = 90°, h = 1.215 m

 

Calculation for the location of support of vertical circular gate

Problem
A vertical circular gate in a tunnel 8 m in diameter has oil (sp. gr. 0.80) on one side and air on the other side as shown in Figure HD-73. If oil is 12 m above the invert and the air pressure is 40 kPa, where will a single support be located to hold the gate in position (above the invert of the gate)?
 

1994-may-hyd-tunnel-gate.jpg

 

A.   1.36 m C.   3.24 m
B.   1.84 m D.   2.62 m

 

Find the approximate height of a mountain by using mercury barometer

Problem
Assuming specific weight of air to be constant at 12 N/m3, what is the approximate height of Mt. Banahaw if a mercury barometer at the base of the mountain reads 654 mm and at the same time another mercury barometer at the top of the mountain reads 480 mm.

A.   1642.3 m C.   3051.4 m
B.   1934.5 m D.   1735.2 m