A long, vertical wall separates seawater from fresh water. If the seawater stands at a depth of \(7 \mathrm{m},\) what depth of freshwater is required to give a zero resultant force on the wall? When the resultent force is zero, will the moment due to the fluid forces be zero? Explain.

Short Answer

Expert verified
To balance the forces exerted by the seawater, a depth of \(7.175 \, \mathrm{m}\) of freshwater is required. However, even with the net force is zero, the wall will experience a non-zero moment due to the different pressure distributions of seawater and freshwater.

Step by step solution

01

Calculations

The pressures exerted by the seawater and freshwater on the wall must be equal for the resultant force to be zero. The pressure due to a fluid column is given by \( P = \rho g h \), where \( \rho \) is the fluid density, \( g \) is acceleration due to gravity, and \( h \) is height of the fluid column. Therefore, the forces from the seawater and freshwater on each side of the wall are indicated and equated for equality. This gives us \( 1025 \times 9.8 \times 7 = 1000 \times 9.8 \times h \). From this equation, we can solve for \( h \).
02

Solving for h

The equation is rearranged and simplified to find the value of \( h \): \( h = \frac{1025 \times 9.8 \times 7}{1000 \times 9.8} = 7.175 \, \mathrm{m} \)
03

Addressing Moment Force

Although the resultant force on the wall is zero, this does not mean the moment due to the fluid forces would also be zero. The moment force is a measure of the rotational effect of the force about a certain point. Even if the resultant force is zero, the different distribution of the forces (due to the different liquid heights) may result in a non-zero moment. In this case, the wall will still be subjected to a bending moment as the depth wise distribution of pressure, hence the resultant force acting on it, are different for seawater and freshwater.

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