The speed of a boat is measured by a pitot tube .Whentraveling in sea water (den

Question

The speed of a boat is measured by a pitot tube .Whentraveling in sea water (density=64 lbm/ft^3), the tube measures apressure of 2.5 lbf/in^2 due to the motion.What is the speed (mph)of the boat? What would be the speed in fresh water (density=62.4lbm/ft^3),also for pressure of 2.5 lbm/in^2?

I know that u=(2*g*h)^1/2 so , can we say P=*g*h and from it find h then use thefirst equation to calculate u ?!! Please help The speed of a boat is measured by a pitot tube .Whentraveling in sea water (density=64 lbm/ft^3), the tube measures apressure of 2.5 lbf/in^2 due to the motion.What is the speed (mph)of the boat? What would be the speed in fresh water (density=62.4lbm/ft^3),also for pressure of 2.5 lbm/in^2?

I know that u=(2*g*h)^1/2 so , can we say P=*g*h and from it find h then use thefirst equation to calculate u ?!! Please help

Explanation / Answer

%u2206P = 2.5 lb_f/ in^2 = 360 lb_f/ft^2
%u03C1 = 64 lb_m/ft^3

%u2206P = 1/2*%u03C1*V^2
V^2 = 2*%u2206P/%u03C1
V = [2*%u2206P/%u03C1]^0.5
V = [2*360 lb_f/ft^2 / 64 lb_m/ft^3]^0.5 = [11.25 lb_f*ft/lb_m]^0.5, note 1 lbf = 1 lbm*32.17 ft/s^2
V = 19.024 ft/s = 12.971 mph (speed of water)

Velocity is relative, so V boat = 12.971 mph

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