The figure shows a crude type of perfume atomizer. When bulb at A is compressed, air flows swiftly through the tube BC with uniform speed v, there by causing a reduced pressure at the top position of vertical tube DE. The liquid of density $$500$$ $$kg/m3$$, then rises in the tube, enters tube BC and sprayed out. When bulb is in natural position the air in the bulb and tube are at atmospheric pressure $$P0=105N/m2$$. When bulb A is compressed, it creates an excess pressure Δ$$p=0.001$$ $$P0$$ inside the bulb A. Density of air is $$1.3$$ $$kg/m3$$. If the magnitude of minimum value of speed v, required to cause the liquid to rise to tube BC is $$5k$$ $$m/s$$. Find the value of k. (g$$ $$=$$ $$10$$ $$m/s2$$ $$).

Question

The figure shows  a  crude  type  of  perfume  atomizer.  When  bulb  at  A  is  compressed,  air  flows swiftly  through  the  tube  BC  with  uniform  speed  v,  there  by  causing  a  reduced  pressure  at  the top position of vertical tube DE. The liquid of density $$500$$ $$kg/m3$$, then rises in the tube, enters tube BC and sprayed out. When bulb is in natural position the air in the bulb and tube are at atmospheric pressure $$P0=105N/m2$$. When bulb A is compressed, it creates an excess pressure Δ$$p=0.001$$  $$P0$$  inside the bulb A.  Density of air is $$1.3$$  $$kg/m3$$.  If the magnitude of  minimum  value  of  speed  v, required to cause the liquid to rise to tube BC is $$5k$$ $$m/s$$. Find the value of k. (g$$ $$=$$ $$10$$ $$m/s2$$ $$).

Infinity Learn · Accepted Answer

Use Bernoulli’s equation at $$point-3$$ and $$point-4$$, we can write $$P0+$$ΔPρ$$air=PBC$$ρ$$air+12v2$$⇒$$PBC=P0+$$ΔP−$$0.65$$  $$v2Using$$ Bernoulli’s equation at $$point-1$$ and $$point-2$$, we can $$writeP1$$ρ$$liquid+12vliquid2=P2$$ρliquid​⇒    $$PBC+$$ρliquidghρ$$liquid+12v$$ℓ$$2=P0$$ρℓ​⇒    $$P0+$$Δ$$P+$$ρℓgh−$$0.65v2$$ρℓ$$+12v$$ℓ$$2=P0$$ρℓ​⇒  $$12$$ρℓvℓ$$2=0.65$$ $$v2$$−ΔP−ρℓgh≥$$0$$​⇒   $$v2$$≥Δ$$P+$$ρℓ$$gh0.65$$​⇒$$vmin=$$Δ$$P+$$ρℓ$$gh0.65=1005=20$$  $$m/s$$

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