Question

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water is flowing through a horizontal pipe. which of the following is true?

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

Explanation:

Step1: Apply Bernoulli's equation

For a horizontal pipe \( y_1 = y_2 \), so Bernoulli's equation \( P_1+\frac{1}{2}
ho v_1^2+
ho g y_1=P_2+\frac{1}{2}
ho v_2^2+
ho g y_2 \) simplifies to \( P_1+\frac{1}{2}
ho v_1^2=P_2+\frac{1}{2}
ho v_2^2 \).

Step2: Analyze velocity relationship

Since the fluid accelerates \( v_1>v_2 \). Rearranging the simplified Bernoulli's equation \( P_2 - P_1=\frac{1}{2}
ho(v_1^2 - v_2^2) \). Because \( v_1>v_2 \), \( P_2 - P_1>0 \), so \( P_2>P_1 \).

Answer:

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