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 1 is greater than in section 2.
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.

Explanation:

Step1: Apply the Bernoulli's equation

Bernoulli's equation is \(P +
ho gh+\frac{1}{2}
ho v^{2}=\text{constant}\). Since the cross - sectional area \(A\) is uniform, from the equation of continuity \(A_1v_1 = A_2v_2\) (where \(A_1 = A_2\)), we get \(v_1=v_2\). So \(\frac{1}{2}
ho v_1^{2}=\frac{1}{2}
ho v_2^{2}\).

Step2: Analyze the pressure - height relationship

Let \(P_1\) and \(P_2\) be the pressures at sections 1 and 2, \(h_1\) and \(h_2\) be the heights. The Bernoulli's equation simplifies to \(P_1+
ho gh_1=P_2+
ho gh_2\). If \(h_2>h_1\) (assuming section 2 is at a higher elevation than section 1), then \(P_1 - P_2=
ho g(h_2 - h_1)>0\) (because \(
ho> 0\), \(g>0\) and \(h_2 - h_1>0\) if 2 is higher).

Answer:

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