Analysis

This question examines the operation rules of complex numbers and the definitions of real and imaginary parts, which is a basic question.

By using the operation rules of complex numbers and the definitions of real and imaginary parts, we can obtain the solution.

Solution

Given the complex number $z= \frac{1+ai}{i}= \frac{(1+ai)i}{i^{2}}=-a+i$,

Since the real part and the imaginary part of $Z$ are equal,

Therefore, $-a=1$,

Solving this, we get $a=-1$. Therefore, $|z|= \sqrt{1+1}= \sqrt{2}$

Hence, the answer is $\boxed{\sqrt{2}}$.