gnoring small-scale oscillations and any environmental disturbances state if the
ID: 1766394 • Letter: G
Question
gnoring small-scale oscillations and any environmental disturbances state if the following flows are steady or not and give reasons in sup- port of your answer: (i) The flow over an aircraft wing, as "seen" by a passenger, from the time the airplane is on the groundl t reaches cruise conditions.ii) Flow through an opening in a rigid tank through which compressed air is escaping into the atmosphere (till the time the pressure in the tank becomes equal to the atmospheric pressure). (iii) Flow taining water (for short times through a small opening at the bottom of a large rigid tank conExplanation / Answer
Case 1. To start with when the plane is at rest on ground there is no airflow. Flow velocity is zero. After that the plane accelerates on ground and so the flow velocity of air over the wing as seen by passenger inside is no longer zero and it increases. It continues to change rather increase with change in direction too as the plane lifts from the ground. The process continues till it cruises when because of plane uniform speed along a straight line the flow over wing will appear steady relative to the passenger inside.
Case 2. The rate of flow through the opening will depend on pressure difference between the rigid tank pressure and pressure outside. Initially because of higher pressure difference the rate of flow will be very high but as more and more air at high pressure escape to atmosphere, the pressure inside the tank will reduce, pr diff between outside and inside will reduce and hence the flow rate will reduce. Finally when there is no pressure diff , flow will stop. So it is essentially unsteady till the flow stops.
Case 3. Here the water will get drained out through a small opening. If the tank is very big compared to the opening for a short duration the water level in the tank will not change. This will mean that the depth of water level at the opening remains constant leading to pressure being constant. This will mean a fixed pressure diff between the opening (inside of tank at the bottom) and atmospheric pressure. For the reason given in case 2 above, the flow rate will remain constant for a short period of time, meaning the flow will be steady.
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