State all assumptions and show working. The gate shown in the figure below is hi

Question

State all assumptions and show working.

The gate shown in the figure below is hinged at the point shown to hold the gate closed. The gate is 3 m wide normal to the plane of the diagram Calculate the force required at A to hold the gate closed. Assume the density of the water is 999 kg/m3. You have noticed that dams are much thicker at the bottom Explain why dams are built that way? For the system shown in in the figure below: What is the flow direction? What kind of machine is at A? Do you think both pipes, AB and CA, are the same diameter Sketch in the EGL for the system Is there a vacuum at any point or region of the pipes? If so, identify the location A pipe system consists of a gate valve, wide open (Kv = 0.2), in line A and a globe valve, wide open (Kv = 10), in line B. The cross-sectional area of pipe A is half of the cross-sectional area of pipe B. The head loss due to the junction, elbows, and pipe friction are negligible compared with the head loss through the valves. Find the ratio of the discharge in line B to that in line A.

Explanation / Answer

Here..I am solving only first question..

Water pressure at hinge = 999*g*1.5 Pascals. This acts uniformly throughout the gate length. So the force due to it acts at mid-point of gate and perpendicular to it.

Depth of water at A = 1.5 + 3Sin30 = 3 m

Water pressure at A = 999*g*3 Pascals.

Difference in pressure at hinge and A is = 999*g*3 - 999*g*1.5 = 999*g*1.5 Pa

The force on gate due to this pressure difference acts in triangular loading form which is 0 at hinge and 999*g*1.5 at A. The force due to it acts at 2/3 length of gate from hinge and normal to gate.

Thus, balancing moments about the hinge,

F*3 = 999*g*1.5*(3*3) *(3/2) + 999*g*1.5 *(3*3)*(2/3*3)

Solving this, F = 154353 N

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