What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 35.0 cm?

First, you find the pressure experience by the car at that depth. This pressure is called the hydraulic pressure with the equation: P=density*gravity*depth. The density of water is 1000 kg/m^3; the acceleration due to gravity is 9.81 m/s^2. So, we need a value for the depth. Suppose, the car was underwater 6 m deep. Then the pressure would be:

Pressure = 1000 kg/m3*9.81 m/s^2*6m = 58,860 Pascals

Pressure, by definition, is the force over unit area. Since we know the are of the circular window, we can therefore determine the force exerted by the water to the car's window.

P = F/A

P=F / (π * (0.35/2) ^2)

58,860 = F/0.0962

F = 5,663 Newtons