The figure shows a vertical pipe of uniform cross-section in which a liquid of ` rho` is flowing upwards. If ` v_A and v_B ` be the velocities of the fluid at points A and B separated by a distance h, `p_A and p_B ` are the respective pressure at the two points, then select the correct option:

Options

A. ` v_B lt v_A `
B. `P_B gt P_A `
C. ` P_A = P _B + rho gh `
D. `P_A gt P_B + rho gh `

Answer

C

Explanation

Applying Bernoulli’s equation
` rho (v_A^ 2 ) /( 2) + 0 + p_A = rho (v_B^ 2 )/( 2 ) + rho gh + p_B `
Since ` V_A = V_B ` from continuity equation, therefore ` P_A= P_B + rho gh `