Knowledge of fluid mechanics
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I want to ask about the water from the faucet: when the flow is reduced, the water flow becomes very slow, almost like a dripping sound, with a very low velocity. But why does the flow speed increase when you cover the open faucet with your hand (even if not completely covered)?
If your hand can cover it completely, there will be no leakage at all, or only a few drops. When the water pressure remains constant, changing the cross-sectional area increases the flow velocity. When the faucet is turned down tightly, the loss through the faucet is significant; at that point the flow rate decreases, and when it is completely closed, no water flows at all. Your hand only changes the cross-sectional area, so it has little effect on the pressure.
Try to explain it, and let’s discuss any issues: Suppose the outlet area of the faucet is A, and the flow area at the knob when the faucet is fully open is B. Depending on the faucet opening, the flow area at the knob ranges from zero to B. Assume that when the open faucet is covered with a hand, the actual outlet area of the faucet is C; let the flow rate at this time be Q, then the outlet flow velocity equals Q/C. When the faucet is adjusted so that the flow area at the knob is C, and the flow rate is denoted as Q, with the faucet not being blocked by hand, the water flow will ultimately exit through the outlet area A of the faucet (there is another special case when the flow rate is so low that it cannot fill the pipe); in this case, the outlet flow velocity equals Q/A. Since when the open faucet is covered with a hand, the actual outlet area C of the faucet is much smaller than A, Q/C is therefore much larger than Q/A; in other words, when an open faucet is covered with a hand (but not completely blocked), the flow velocity is very high. When covering a faucet at any opening with the hand, the flow rate decreases, but since the area through which the fluid flows is reduced by more, the flow velocity increases. When the faucet is turned wide open, the actual flow area at the knob increases, which reduces resistance and thus increases the flow rate. Since the outlet area A of the faucet remains unchanged, the exit flow velocity increases.