An example internal relief valve disclosed herein includes a relief valve seat coupled to a first end of the relief valve stem and to engage a first side of a sensing apparatus to prevent fluid flow between the first side of the sensing apparatus and a second side of the sensing apparatus when the internal relief valve is in a closed position. A bleed hole within a surface of the sensing apparatus and separate from the opening of the sensing apparatus is dimensioned to provide a controlled flow rate between the first side and the second side of the sensing apparatus when the internal relief valve is in an open position. A seal is disposed along a body of the relief valve stem upstream from the bleed hole and the valve seat to prevent fluid flow between the first side of the sensing apparatus and the second side of the sensing apparatus via the opening of the sensing apparatus when the relief valve is in the open position.