1. Idea: The two conducting $U$-tubes together form a closed rectangular circuit.

2. Magnetic flux method: Since the magnetic field $B$ is perpendicular to the plane, the induced emf is $\mathcal E=-\frac{d\Phi}{dt}=-B\frac{dA}{dt}$ where $A$ is the area enclosed by the circuit.

3. Change of area:

   • The width of the tubes is $l$.
   • As each tube moves toward the other with speed $v$, the separation between the two vertical conducting sides decreases.
   • Since both are moving, the relative speed of approach is $v+v=2v.$

4. Therefore, the enclosed area decreases at the rate $\frac{dA}{dt}= -l(2v).$ Negative sign appears because area is shrinking.

5. Substitute into Faraday's law: $\mathcal E=-B\left(-2lv\right)=2Blv.$

6. Hence the magnitude of induced emf is $\boxed{2Blv}.$

7. Option check:

   • A: $-Blv$ — incorrect
   • B: $blv$ — incorrect
   • C: $2Blv$ — correct
   • D: zero — incorrect

So the correct option is C.