- #1
wahaj
- 154
- 2
Homework Statement
A cart is acclerating to the right with a=3m/s^2. Fluid is in hydrostatic state. Find the force on the back wall. Cart goes .8m into the page. In the image dotted line is free surface when cart is stationary.
Homework Equations
\vec{\nabla P}=\rho (\vec{g} - \vec{a} ) \\<br /> dP = d \vec{R} \bullet \vec{\nabla P} \\<br /> F = \iint P \hat{n} dA
The Attempt at a Solution
\int_1^2 dP = \int_1^2 d \vec{R} \bullet \vec{\nabla P} \\ <br /> \int_1^2 dP = \int_1^2 (dx \hat{i} + dz \hat{k}) \bullet \rho (-g \hat{k} - a \hat{i} ) \\ <br /> P_2 - P_1 = - \rho g(z_2 - z_1) - \rho a (x_2 - x_1) \\ <br /> P_2 - P_1 = 0-0 = 0 \\ <br /> g(z_2 - z_1) = a (x_2 - x_1) \\ <br /> x_2 = 2 \ ; \ x_1 = 0 \ ; \ z_2 = 0.5+h \ ; \ z_1 = 0.5-h \\<br /> g(2h) = a(2) \\ <br /> h = 3/9.81 = 0.3058 m \\ <br /> <br /> F = \iint P \hat{n} dA \\ <br /> P = -\rho g z + C \\ <br /> P= \rho g \ when \ z = 0 \\ <br /> \rho g = C \\ <br /> P = \rho g (1-z) \\ <br /> F = \int_0^.8 \int_0^.8058 \rho g (1-z) \hat{i} dzdy \\<br /> F = 3.776 kN
The actual answer is 2.55 kN. I think my mistake lies in me not including the pressure due to the cart accelerating to the right. How would I account for that acceleration?
