Question

Water is flowing in streamline motion through a tube with its axis horizontal. Consider two points A and B in the tube at the same horizontal level. 

(a) The pressures at A and B are equal for any shape of the tube. 

(b) The pressures are never equal. 

(c) The pressures are equal if the tube has a uniform cross-section. 

(d) The pressures may be equal even if the tube has a nonuniform cross-section.

Answer 1

(c) The pressures are equal if the tube has a uniform cross-section.

(d) The pressures may be equal even if the tube has a nonuniform cross-section.

EXPLANATION: 

According to the Bernoulli's theorem if the height of the points is the same the pressure will be more where the speed is less.           

If the tube is of any shape the velocities at A and B may vary. Hence pressure at A and B will not be equal. Option (a) is not true.         

If we do not know the shape of the tube and the cross-section at A and B, the pressures at A and B may vary. Option (b) is not true.          

If the tube has uniform cross-section the velocity, in this case, will be equal everywhere so the pressures are also equal. Option (c) is true.          

If the cross-section of the tube is non-uniform there may be a chance that the areas of the cross-sections at A and B are the same. In that case, the velocities at A and B will be the same and hence the pressure. Option (d) is true.