Question

a fluid flowing in a pipe with a uniform cross - sectional area changes elevation. which of the following is true?
the pressure in the fluid in section 2 is greater than in section 1.
the pressure in the fluid in section 1 and 2 is the same.
the pressure in the fluid in section 1 is greater than in section 2.

Explanation:

Step1: Apply the continuity equation

Since the cross - sectional area \(A\) is uniform (\(A_1 = A_2\)), from the continuity equation \(A_1v_1=A_2v_2\), we get \(v_1 = v_2\).

Step2: Apply Bernoulli's equation

Bernoulli's equation is \(P_1+
ho gh_1+\frac{1}{2}
ho v_1^{2}=P_2+
ho gh_2+\frac{1}{2}
ho v_2^{2}\). Because \(v_1 = v_2\), the equation simplifies to \(P_1+
ho gh_1=P_2+
ho gh_2\). Rearranging gives \(P_1 - P_2=
ho g(h_2 - h_1)\). Since \(h_2>h_1\) (assuming section 2 is at a higher elevation than section 1), \(
ho g(h_2 - h_1)>0\), so \(P_1>P_2\).

Answer:

The pressure in the fluid in section 1 is greater than in section 2.