Question

Fig shows an arrangment used to make water flow through a horizontal capillary tube LM using a water bottle. Which of the following statements is correct?

(1) Rate of flow of water is constant till level of water in water bottle falls upto point O

(2) Rate of flow of water decreases as level of water in water bottle decreases upto point O

(3) Rate of flow of water is constant till water level in bottle decreases upto point A and then decreases as water level falls upto O

(4) Rate of flow of water decreaes till water level in bottle decreases upto point A and then is constant till water level decreases upto O

Answer 1

(3) Rate of flow of water is constant till water level in bottle decreases upto point A and then decreases as water level falls upto O

Let h be the instantaneous height of water above point A. P₀ is atmospheric pressure. P_A = pressure of liquid in bottle at level A = P₀

P = Pressure of liquid at opening O

= P_A + (H₀ – h)p g = P₀ +( H´) p g; where H₀ – h = H´ = OA

Pressure P is constant till water level in water bottle reaches point A. Therefore rate of flow of water in capillary tube is constant. If level of water in bottle goes below point A; pressure at O does not remain constant. It is equal to P₀ + pressure due to water column above O but below A. Since pressure at inlet of capillary tube varies (decreases) the rate of flow of water in capillary tube also decreaes.