Question

Q1.A perfectly balanced weight and platform are supported by a steady water jet as shown in the figure below. If the total weight supported is 900 N, determine the jet velocity. Diameter of the water jet is 5 cm.

Please help me

Answer 1

$F = 900N \\ d = 5cm = 5 \cdot 10^{-2}m\\ \rho = 1000 \frac{kg}{m^3} \\ \pi \approx 3.14$

$F_p = F_w = F$

Newton's second law => $F\Delta t = mv$ (*)

Where $m = V\cdot\rho$, because of $V = S\cdot h = S\cdot v\Delta t = \pi\cdot (\frac{d}{2})^2 \cdot v\Delta t$

$$F\Delta t = v \cdot \rho \cdot \pi\cdot (\frac{d}{2})^2 \cdot v\Delta t$$

$$F = \rho \cdot \pi\cdot (\frac{d}{2})^2 \cdot v^2$$

$$v^2 = \frac{F}{\rho \pi \cdot (\frac {d}{2})^2} = \frac{900N}{1000\frac{kg}{m^3} \cdot 3.14 \cdot (\frac {5 \cdot 10^{-2}} {2})^2m^2} = 458.5987 (\frac{m}{s})^2$$

Then the answer:

$$v = 21.415 \frac{m}{s}$$

(*):

$F = ma \\ F = m\frac{v - 0}{\Delta t} \\ F \Delta t = mv$