Whenever possible I almost always photograph running water using slow shutter exposure. But to do it under bright ambient light, it means using a tripod and several stops of ND filter. The tripod, you need to handle the camera shake during long exposure. The ND filter, you need to significantly cut down the bright ambient light going in to your camera's sensor. Tripods are not allowed inside the Museum of Islamic Arts in Qatar (where this picture was taken) but you could probably get away with a mini-tripod or one of those Gorilla pods if you use them very, very discreetly.
I took this photo with a Fujifilm X100S at 1/2 second, f/16 and ISO 100 - handheld. That camera has a built-in 3-stops ND filter which allowed me to drop that shutter speed that slow. I could shoot it slower with smaller aperture but that is as slow as I can hold the camera steady. Yup, handheld at 1/2 second. No image stabilizer here, just my "steady" hands. I can do that because the X100 has a near vibration free leaf shutter and without a pelical mirror to cause vibration.
Next time, I'm gonna use a mini-tripod to shoot even slower.