Question

An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity $v$ (in m/s) of the fluid is __.

Answer 1

1

Answer 2

The principle of conservation of mass for an incompressible fluid implies that the volume flow rate is conserved. Thus, the flow rate at the inlet equals the sum of the flow rates at the outlets. The volume flow rate is given by the product of the cross-sectional area and the fluid velocity. $A_1 v_1 = A_2 v_2 + A_3 v_3$ Given $A_1=A, v_1=3$ m/s, $A_2=A, v_2=1.5$ m/s, and $A_3=1.5A$. Substituting these values: $A \times 3 = A \times 1.5 + 1.5A \times v$ Simplifying the equation: $3 = 1.5 + 1.5v$ $1.5 = 1.5v$ $v = 1 \text{ m/s}$