How much  dead load required to compress the water to up word? ?

water does not compress to any appreciable degree. I think what you are asking what is the weight/mass required to raise the water to the height shown.

the height of the water above the piston is 40 ft – 90 cm – some other numbers that are unknown.  Such as thickness of piston, and height of that U curve at the bottom. that is 12.2 m – 0.9 m - (say 0.5 m) = 10 m at a guess.

The cross sectional area of the 6 cm tube is πr² = π(0.03)² = 0.0028 m²

the cross sectional area of the piston is unknown, say it is 100 cm diameter, A = π(0.5)² = 0.8 m² (at a guess)

pressures have to balance.

That due to long column is:

volume of water in column is 0.0028 m² x 10 m = 0.028 m³

mass of that water is 998 kg/m³ x 0.028 m³ = 28 kg

weight of that water is 28 kg x 9.8 N/kg = 270 N

pressure is 270 N / 0.0028 m² = 98000 N/m² = 98000 Pa

weight required to produce that same pressure at the piston is

W / 0.8 m² = 98000 N/m²

W = 78000 N

mass = 78000 N / 9.8 N.kg = 8000 kg <-----

density of fresh water at 20C = 0.998 g/cm³ = 0.998 kg/L     = 998 kg/m³ = 8.33 lb/gal = 62.1 lb/ft³

Dear in my figure I mensioned dia of piston is 15cm, it is not 100 cm, thank you sir, I never forget you, you are super brilient,