Project ForgeA tube of uniform diameter D is immersed in a steady flowing inviscid liquid stream of velocity V, as shown in the figure (the tube's horizontal inlet is submerged at depth h1 below the free surface of the stream, and its open vertical outlet is at height h2 above the free surface, discharging to atmosphere P_atm). Gravitational acceleration is represented by g. The volume flow rate through the tube is ______.
- A(π/4)D²V
- B(π/4)D²√(2gh2)
- C(π/4)D²√(2g(h1+h2))
- (π/4)D²√(V²−2gh2)
Explanation
Apply Bernoulli's equation along a streamline from a point in the free stream at the tube's inlet depth (pressure p_atm+ρgh1, velocity V, taken as the elevation datum) to the tube's open exit (pressure p_atm, velocity v_exit, elevation h1+h2 above the datum): p_atm+ρgh1+½ρV² = p_atm+½ρv_exit²+ρg(h1+h2). The p_atm and ρgh1 terms cancel, leaving ½ρV²−ρgh2 = ½ρv_exit², so v_exit=√(V²−2gh2). Flow rate Q = (π/4)D²·v_exit = (π/4)D²√(V²−2gh2).
Source: GATE ME 2022 Session 2 (ME-2) (2022)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.